// Numbas version: finer_feedback_settings {"name": "Construir la tabla de verdad de una proposici\u00f3n compuesta", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Construir la tabla de verdad de una proposici\u00f3n compuesta", "tags": [], "metadata": {"description": "

Crear una tabla de verdad para una expresión lógica de la forma :

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                $( a \\ {op1} \\ b) \\ {op2} \\ (c \\ {op} \\ d) \\ {op4} \\ e $

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donde cada una de $a, \\; b, \\; c, \\; d, \\; e, \\; f $ puede ser una de las variables booleanas $ p, \\; q, \\; \\neg q, \\; \\neg p $ y cada uno de los operados $\\{op}$  puede ser uno de los operadores $\\lor, \\; \\land, \\; \\to$.

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Por ejemplo: $((q \\lor \\neg r) \\to (p \\land \\neg q)) \\land \\neg r$
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", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

Dada la proposición compuesta, construya  su tabla de verdad:

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\\[(\\var{a} \\var{op} \\var{b}) \\var{op1}(\\var{a1} \\var{op2} \\var{b1})) \\var{op4}\\var{a2}\\]

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Ingrese V si es verdadero, de lo contrario ingrese F.

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", "advice": "

Primero encontramos la tabla de verdad para: $\\var{a} \\var{op} \\var{b}$:

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$p$$q$$r$$\\var{a} \\var{op} \\var{b}$
$\\var{p[0]}$$\\var{q[0]}$$\\var{r[0]}$$\\var{ev1[0]}$
$\\var{p[1]}$$\\var{q[1]}$$\\var{r[1]}$$\\var{ev1[1]}$
$\\var{p[2]}$$\\var{q[2]}$$\\var{r[2]}$$\\var{ev1[2]}$
$\\var{p[3]}$$\\var{q[3]}$$\\var{r[3]}$$\\var{ev1[3]}$
$\\var{p[4]}$$\\var{q[4]}$$\\var{r[4]}$$\\var{ev1[4]}$
$\\var{p[5]}$$\\var{q[5]}$$\\var{r[5]}$$\\var{ev1[5]}$
$\\var{p[6]}$$\\var{q[6]}$$\\var{r[6]}$$\\var{ev1[6]}$
$\\var{p[7]}$$\\var{q[7]}$$\\var{r[7]}$$\\var{ev1[7]}$
\n

Entonces la tabla de verdad para $\\var{a1} \\var{op2} \\var{b1}$ es:

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$p$$q$$r$$\\var{a1} \\var{op2} \\var{b1}$
$\\var{p[0]}$$\\var{q[0]}$$\\var{r[0]}$$\\var{ev2[0]}$
$\\var{p[1]}$$\\var{q[1]}$$\\var{r[1]}$$\\var{ev2[1]}$
$\\var{p[2]}$$\\var{q[2]}$$\\var{r[2]}$$\\var{ev2[2]}$
$\\var{p[3]}$$\\var{q[3]}$$\\var{r[3]}$$\\var{ev2[3]}$
$\\var{p[4]}$$\\var{q[4]}$$\\var{r[4]}$$\\var{ev2[4]}$
$\\var{p[5]}$$\\var{q[5]}$$\\var{r[5]}$$\\var{ev2[5]}$
$\\var{p[6]}$$\\var{q[6]}$$\\var{r[6]}$$\\var{ev2[6]}$
$\\var{p[7]}$$\\var{q[7]}$$\\var{r[7]}$$\\var{ev2[7]}$
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Juntando estos datos obtenemos     $(\\var{a} \\var{op} \\var{b})\\var{op1}(\\var{a1} \\var{op2} \\var{b1})$:

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\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$p$$q$$r$$\\var{a} \\var{op} \\var{b}$$\\var{a1} \\var{op2} \\var{b1}$$(\\var{a} \\var{op} \\var{b})\\var{op1}(\\var{a1} \\var{op2} \\var{b1})$
$\\var{p[0]}$$\\var{q[0]}$$\\var{r[0]}$$\\var{ev1[0]}$$\\var{ev2[0]}$$\\var{t_value[0]}$
$\\var{p[1]}$$\\var{q[1]}$$\\var{r[1]}$$\\var{ev1[1]}$$\\var{ev2[1]}$$\\var{t_value[1]}$
$\\var{p[2]}$$\\var{q[2]}$$\\var{r[2]}$$\\var{ev1[2]}$$\\var{ev2[2]}$$\\var{t_value[2]}$
$\\var{p[3]}$$\\var{q[3]}$$\\var{r[3]}$$\\var{ev1[3]}$$\\var{ev2[3]}$$\\var{t_value[3]}$
$\\var{p[4]}$$\\var{q[4]}$$\\var{r[4]}$$\\var{ev1[4]}$$\\var{ev2[4]}$$\\var{t_value[4]}$
$\\var{p[5]}$$\\var{q[5]}$$\\var{r[5]}$$\\var{ev1[5]}$$\\var{ev2[5]}$$\\var{t_value[5]}$
$\\var{p[6]}$$\\var{q[6]}$$\\var{r[6]}$$\\var{ev1[6]}$$\\var{ev2[6]}$$\\var{t_value[6]}$
$\\var{p[7]}$$\\var{q[7]}$$\\var{r[7]}$$\\var{ev1[7]}$$\\var{ev2[7]}$$\\var{t_value[7]}$
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A continuación encontramos la tabla de verdad para $\\var{a2}$:

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$\\var{c2}$$\\var{a2}$
$\\var{d2[0]}$$\\var{ev3[0]}$
$\\var{d2[1]}$$\\var{ev3[1]}$
$\\var{d2[2]}$$\\var{ev3[2]}$
$\\var{d2[3]}$$\\var{ev3[3]}$
$\\var{d2[4]}$$\\var{ev3[4]}$
$\\var{d2[5]}$$\\var{ev3[5]}$
$\\var{d2[6]}$$\\var{ev3[6]}$
$\\var{d2[7]}$$\\var{ev3[7]}$
\n

Poniendo todo junto para obtener la tabla de verdad que queremos:

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$p$$q$$r$$(\\var{a} \\var{op} \\var{b})\\var{op1}(\\var{a1} \\var{op2} \\var{b1})$$\\var{a2}$$((\\var{a} \\var{op} \\var{b})\\var{op1}(\\var{a1} \\var{op2} \\var{b1}))\\var{op4}\\var{a2} $
$\\var{p[0]}$$\\var{q[0]}$$\\var{r[0]}$$\\var{t_value[0]}$$\\var{ev3[0]}$$\\var{final_value[0]}$
$\\var{p[1]}$$\\var{q[1]}$$\\var{r[1]}$$\\var{t_value[1]}$$\\var{ev3[1]}$$\\var{final_value[1]}$
$\\var{p[2]}$$\\var{q[2]}$$\\var{r[2]}$$\\var{t_value[2]}$$\\var{ev3[2]}$$\\var{final_value[2]}$
$\\var{p[3]}$$\\var{q[3]}$$\\var{r[3]}$$\\var{t_value[3]}$$\\var{ev3[3]}$$\\var{final_value[3]}$
$\\var{p[4]}$$\\var{q[4]}$$\\var{r[4]}$$\\var{t_value[4]}$$\\var{ev3[4]}$$\\var{final_value[4]}$
$\\var{p[5]}$$\\var{q[5]}$$\\var{r[5]}$$\\var{t_value[5]}$$\\var{ev3[5]}$$\\var{final_value[5]}$
$\\var{p[6]}$$\\var{q[6]}$$\\var{r[6]}$$\\var{t_value[6]}$$\\var{ev3[6]}$$\\var{final_value[6]}$
$\\var{p[7]}$$\\var{q[7]}$$\\var{r[7]}$$\\var{t_value[7]}$$\\var{ev3[7]}$$\\var{final_value[7]}$
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values", "definition": "bool_to_label(list_to_boolean(list(logic_values[1])))", "description": "", "templateType": "anything"}, "ev2": {"name": "ev2", "group": "Second Bracket", "definition": "bool_to_label(pre_ev2)", "description": "", "templateType": "anything"}, "op2": {"name": "op2", "group": "Second Bracket", "definition": "latex(random(\"\\\\lor\",\"\\\\land\",\"\\\\to\"))", "description": "", "templateType": "anything"}, "op4": {"name": "op4", "group": "Ungrouped variables", "definition": "latex(random(\"\\\\lor\",\"\\\\land\",\"\\\\to\"))", "description": "", "templateType": "anything"}, "final_value": {"name": "final_value", "group": "Ungrouped variables", "definition": "bool_to_label(pre_final_value)", "description": "", "templateType": "anything"}, "ev1": {"name": "ev1", "group": "First Bracket", "definition": "bool_to_label(pre_ev1)", "description": "", "templateType": "anything"}, "pre_t_value": {"name": "pre_t_value", "group": "First and Second Brackets", "definition": "map(evaluate(pre_ev1[t]+\" \"+conv(op1)+\" \"+pre_ev2[t],[]),t,0..7)", "description": "", "templateType": "anything"}, "c2": {"name": "c2", "group": "Last ", "definition": "latex(switch(a2=\"\\\\neg p\",\"p\",a2=\"\\\\neg q\",\"q\",\"r\"))", "description": "", "templateType": "anything"}, "pre_ev3": {"name": "pre_ev3", "group": "Last ", "definition": "map(evaluate(convch(a2),[bool_p[t],bool_q[t],bool_r[t]]),t,0..7)", "description": "", "templateType": "anything"}, "latex_symbol_list": {"name": "latex_symbol_list", "group": "Lists of symbols", "definition": "[\"p\",\"q\",\"\\\\neg p\",\"\\\\neg q\",\"r\",\"\\\\neg r\"]", "description": "", "templateType": "anything"}, "op": {"name": "op", "group": "First Bracket", "definition": "latex(random(\"\\\\lor\",\"\\\\land\",\"\\\\to\"))", "description": "", "templateType": "anything"}, "a1": {"name": "a1", "group": "Second Bracket", "definition": "latex(latex_symbol_list[s[2]])", "description": "", "templateType": "anything"}, "bool_q": {"name": "bool_q", "group": "Truth values", "definition": "list_to_boolean(list(logic_values[1]))", "description": "", "templateType": "anything"}, "pre_ev1": {"name": "pre_ev1", "group": "First Bracket", "definition": "map(evaluate(convch(a)+\" \"+conv(op)+\" \"+convch(b),[bool_p[t],bool_q[t],bool_r[t]]),t,0..7)", "description": "", "templateType": "anything"}, "bool_r": {"name": "bool_r", "group": "Truth values", "definition": "list_to_boolean(list(logic_values[2]))", "description": "", "templateType": "anything"}, "r": {"name": "r", "group": "Truth values", "definition": "bool_to_label(list_to_boolean(list(logic_values[2])))", "description": "", "templateType": "anything"}, "ev3": {"name": "ev3", "group": "Last ", "definition": "bool_to_label(pre_ev3)", "description": "", "templateType": "anything"}, "d2": {"name": "d2", "group": "Last ", "definition": "switch(a2=\"\\\\neg p\",p,a2=\"\\\\neg q\",q,r)", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "First Bracket", "definition": "latex(latex_symbol_list[s[1]])", "description": "", "templateType": "anything"}, "b1": {"name": "b1", "group": "Second Bracket", "definition": "latex(latex_symbol_list[s[3]])", "description": "", "templateType": "anything"}, "pre_ev2": {"name": "pre_ev2", "group": "Second Bracket", "definition": "map(evaluate(convch(a1)+\" \"+conv(op2)+\" \"+convch(b1),[bool_p[t],bool_q[t],bool_r[t]]),t,0..7)", "description": "", "templateType": "anything"}, "logic_values": {"name": "logic_values", "group": "Ungrouped variables", "definition": "transpose(matrix(cart(3)))", "description": "", "templateType": "anything"}, "s": {"name": "s", "group": "Lists of symbols", "definition": "repeat(random(0..5),6)", "description": "", "templateType": "anything"}, "a2": {"name": "a2", "group": "Last ", "definition": "latex(random(\"\\\\neg p\",\"\\\\neg q\",\"\\\\neg r\"))", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "First Bracket", "definition": "latex(latex_symbol_list[s[0]])", "description": "", "templateType": "anything"}, "p": {"name": "p", "group": "Truth values", "definition": "bool_to_label(list_to_boolean(list(logic_values[0])))", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "a1 <>b1 and\nif(a='p' or a='\\\\neg p',b=random('q','\\\\neg q'),b=random('p','\\\\neg p'))\n", "maxRuns": "150"}, "ungrouped_variables": ["pre_final_value", "op4", "logic_values", "final_value"], "variable_groups": [{"name": "Lists of symbols", "variables": ["logic_symbol_list", "latex_symbol_list", "s"]}, {"name": "First Bracket", "variables": ["a", "b", "op", "pre_ev1", "ev1"]}, {"name": "Second Bracket", "variables": ["a1", "b1", "op2", "pre_ev2", "ev2"]}, {"name": "Truth values", "variables": ["p", "q", "r", "bool_p", "bool_q", "bool_r"]}, {"name": "Last ", "variables": ["a2", "pre_ev3", "c2", "d2", "ev3"]}, {"name": "First and Second Brackets", "variables": ["op1", "pre_t_value", "t_value"]}], "functions": {"conv": {"parameters": [["op", "string"]], "type": "string", "language": "jme", "definition": "switch(op=\"\\\\land\",\"and\",op=\"\\\\lor\",\"or\",\"implies\")"}, "evaluate": {"parameters": [["expr", "string"], ["dependencies", "list"]], "type": "number", "language": "javascript", "definition": "return scope.evaluate(expr);"}, "cart": {"parameters": [["n", "number"]], "type": "number", "language": "jme", "definition": "if(n=2,[[true,true],[true,false],[false,true],[false,false]],map([true]+cart(n-1)[x],x,0..2^(n-1)-1)+map([false]+cart(n-1)[x],x,0..2^(n-1)-1))"}, "list_to_boolean": {"parameters": [["l", "list"]], "type": "list", "language": "jme", "definition": "map(if(l[x]<>0,true,false),x,0..length(l)-1)"}, "bool_to_label": {"parameters": [["l", "list"]], "type": "number", "language": "jme", "definition": "map(if(l[x],'V','F'),x,0..length(l)-1)"}, "convch": {"parameters": [["ch", "string"]], "type": "string", "language": "jme", "definition": "switch(ch=\"\\\\neg p\",\"not bool_p[t]\",ch=\"\\\\neg q\",\"not bool_q[t]\",ch=\"p\",\"bool_p[t]\",ch=\"q\",\"bool_q[t]\",ch=\"r\",\"bool_r[t]\",\"not bool_r[t]\")"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Completa la siguiente tabla de verdad:

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$ p $$ q $$ r $$ (\\var {a} \\var{op} \\var{b}) \\var {op1} (\\var {a1} \\var {op2} \\var {b1}) \\var {op4} \\var {a2} $
$ \\var {p [0]} $$ \\var {q [0]} $$ \\var {r [0]} $[[0]]
$ \\var {p [1]} $$ \\var {q [1]} $$ \\var {r [1]} $[[1]]
$ \\var {p [2]} $$ \\var {q [2]} $$ \\var {r [2]} $[[2]]
$ \\var {p [3]} $$ \\var {q [3]} $$ \\var {r [3]} $[[3]]
$ \\var {p [4]} $$ \\var {q [4]} $$ \\var {r [4]} $[[4]]
$ \\var {p [5]} $$ \\var {q [5]} $$ \\var {r [5]} $[[5]]
$ \\var {p [6]} $$ \\var {q [6]} $$ \\var {r [6]} $[[6]]
$ \\var {p [7]} $$ \\var {q [7]} $$ \\var {r [7]} $[[7]]
", "gaps": [{"type": "patternmatch", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{final_value[0]}", "displayAnswer": "{final_value[0]}", "matchMode": "regex"}, {"type": "patternmatch", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{final_value[1]}", "displayAnswer": "{final_value[1]}", "matchMode": "regex"}, {"type": "patternmatch", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{final_value[2]}", "displayAnswer": "{final_value[2]}", "matchMode": "regex"}, {"type": "patternmatch", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{final_value[3]}", "displayAnswer": "{final_value[3]}", "matchMode": "regex"}, {"type": "patternmatch", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{final_value[4]}", "displayAnswer": "{final_value[4]}", "matchMode": "regex"}, {"type": "patternmatch", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{final_value[5]}", "displayAnswer": "{final_value[5]}", "matchMode": "regex"}, {"type": "patternmatch", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{final_value[6]}", "displayAnswer": "{final_value[6]}", "matchMode": "regex"}, {"type": "patternmatch", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{final_value[7]}", "displayAnswer": "{final_value[7]}", "matchMode": "regex"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Luis Hernandez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2870/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Luis Hernandez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2870/"}]}