// Numbas version: exam_results_page_options {"name": "Truth tables 3 ", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variablesTest": {"condition": "a1 <>b1 and a2<>b2 and\nif(a='p' or a='\\\\neg p',b=random('q','\\\\neg q'),b=random('p','\\\\neg p'))\n", "maxRuns": "150"}, "tags": [], "variables": {"ev3": {"description": "", "templateType": "anything", "group": "Third Bracket", "definition": "bool_to_label(pre_ev3)", "name": "ev3"}, "ev2": {"description": "", "templateType": "anything", "group": "Second Bracket", "definition": "bool_to_label(pre_ev2)", "name": "ev2"}, "a2": {"description": "", "templateType": "anything", "group": "Third Bracket", "definition": "latex(latex_symbol_list[s[4]])", "name": "a2"}, "disq": {"description": "", "templateType": "anything", "group": "Truth values", "definition": "bool_to_label(q)", "name": "disq"}, "pre_ev2": {"description": "", "templateType": "anything", "group": "Second Bracket", "definition": "map(evaluate(convch(a1)+\" \"+conv(op2)+\" \"+convch(b1),[p[t],q[t]]),t,0..3)", "name": "pre_ev2"}, "op2": {"description": "", "templateType": "anything", "group": "Second Bracket", "definition": "latex(random(\"\\\\lor\",\"\\\\land\",\"\\\\to\"))", "name": "op2"}, "disp": {"description": "", "templateType": "anything", "group": "Truth values", "definition": "bool_to_label(p)", "name": "disp"}, "op": {"description": "", "templateType": "anything", "group": "First Bracket", "definition": "latex(random(\"\\\\lor\",\"\\\\land\",\"\\\\to\"))", "name": "op"}, "a1": {"description": "", "templateType": "anything", "group": "Second Bracket", "definition": "latex(latex_symbol_list[s[2]])", "name": "a1"}, "op1": {"description": "", "templateType": "anything", "group": "First and Second Brackets", "definition": "latex(random(\"\\\\lor\",\"\\\\land\",\"\\\\to\"))", "name": "op1"}, "b2": {"description": "", "templateType": "anything", "group": "Third Bracket", "definition": "latex(latex_symbol_list[s[5]])", "name": "b2"}, "p": {"description": "", "templateType": "anything", "group": "Truth values", "definition": "[true,true,false,false]", "name": "p"}, "pre_t_value": {"description": "", "templateType": "anything", "group": "First and Second Brackets", "definition": "map(evaluate(pre_ev1[t]+\" \"+conv(op1)+\" \"+pre_ev2[t],[]),t,0..3)", "name": "pre_t_value"}, "op4": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "latex(random(\"\\\\lor\",\"\\\\land\",\"\\\\to\"))", "name": "op4"}, "latex_symbol_list": {"description": "", "templateType": "anything", "group": "Lists of symbols", "definition": "[\"p\",\"q\",\"\\\\neg p\",\"\\\\neg q\"]", "name": "latex_symbol_list"}, "op3": {"description": "", "templateType": "anything", "group": "Third Bracket", "definition": "latex(random(\"\\\\lor\",\"\\\\land\",\"\\\\to\"))", "name": "op3"}, "pre_ev1": {"description": "", "templateType": "anything", "group": "First Bracket", "definition": "map(evaluate(convch(a)+\" \"+conv(op)+\" \"+convch(b),[p[t],q[t]]),t,0..3)", "name": "pre_ev1"}, "b": {"description": "", "templateType": "anything", "group": "First Bracket", "definition": "latex(latex_symbol_list[s[1]])", "name": "b"}, "pre_ev3": {"description": "", "templateType": "anything", "group": "Third Bracket", "definition": "map(evaluate(convch(a2)+\" \"+conv(op3)+\" \"+convch(b2),[p[t],q[t]]),t,0..3)", "name": "pre_ev3"}, "logic_symbol_list": {"description": "", "templateType": "anything", "group": "Lists of symbols", "definition": "[\"p\",\"q\",\"not p\",\"not q\"]", "name": "logic_symbol_list"}, "t_value": {"description": "", "templateType": "anything", "group": "First and Second Brackets", "definition": "bool_to_label(pre_t_value)", "name": "t_value"}, "s": {"description": "", "templateType": "anything", "group": "Lists of symbols", "definition": "repeat(random(0..3),6)", "name": "s"}, "ev1": {"description": "", "templateType": "anything", "group": "First Bracket", "definition": "bool_to_label(pre_ev1)", "name": "ev1"}, "final_value": {"description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "bool_to_label(map(evaluate(pre_t_value[t]+\" \"+conv(op4)+\" \"+pre_ev3[t],[]),t,0..3))", "name": "final_value"}, "a": {"description": "", "templateType": "anything", "group": "First Bracket", "definition": "latex(latex_symbol_list[s[0]])", "name": "a"}, "b1": {"description": "", "templateType": "anything", "group": "Second Bracket", "definition": "latex(latex_symbol_list[s[3]])", "name": "b1"}, "q": {"description": "", "templateType": "anything", "group": "Truth values", "definition": "[true,false,true,false]", "name": "q"}}, "name": "Truth tables 3 ", "advice": "

First we find the truth table for $\\var{a} \\var{op} \\var{b}$:

\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
$p$$q$$\\var{a} \\var{op} \\var{b}$
$\\var{disp[0]}$$\\var{disq[0]}$$\\var{ev1[0]}$
$\\var{disp[1]}$$\\var{disq[1]}$$\\var{ev1[1]}$
$\\var{disp[2]}$$\\var{disq[2]}$$\\var{ev1[2]}$
$\\var{disp[3]}$$\\var{disq[3]}$$\\var{ev1[3]}$
\n

Then the truth table for $\\var{a1} \\var{op2} \\var{b1}$:

\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$$q$$\\var{a1} \\var{op2} \\var{b1}$
$\\var{disp[0]}$$\\var{disq[0]}$$\\var{ev2[0]}$
$\\var{disp[1]}$$\\var{disq[1]}$$\\var{ev2[1]}$
$\\var{disp[2]}$$\\var{disq[2]}$$\\var{ev2[2]}$
$\\var{disp[3]}$$\\var{disq[3]}$$\\var{ev2[3]}$
\n

Putting these together to find $(\\var{a} \\var{op} \\var{b})\\var{op1}(\\var{a1} \\var{op2} \\var{b1})$:

\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$$q$$\\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{disp[0]}$$\\var{disq[0]}$$\\var{ev1[0]}$$\\var{ev2[0]}$$\\var{t_value[0]}$
$\\var{disp[1]}$$\\var{disq[1]}$$\\var{ev1[1]}$$\\var{ev2[1]}$$\\var{t_value[1]}$
$\\var{disp[2]}$$\\var{disq[2]}$$\\var{ev1[2]}$$\\var{ev2[2]}$$\\var{t_value[2]}$
$\\var{disp[3]}$$\\var{disq[3]}$$\\var{ev1[3]}$$\\var{ev2[3]}$$\\var{t_value[3]}$
\n

Next we find the truth table for $\\var{a2} \\var{op3} \\var{b2}$:

\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$$q$$\\var{a2} \\var{op3} \\var{b2}$
$\\var{disp[0]}$$\\var{disq[0]}$$\\var{ev3[0]}$
$\\var{disp[1]}$$\\var{disq[1]}$$\\var{ev3[1]}$
$\\var{disp[2]}$$\\var{disq[2]}$$\\var{ev3[2]}$
$\\var{disp[3]}$$\\var{disq[3]}$$\\var{ev3[3]}$
\n

Putting this all together to obtain the truth table we want:

\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$$q$$(\\var{a} \\var{op} \\var{b})\\var{op1}(\\var{a1} \\var{op2} \\var{b1})$$\\var{a2} \\var{op3} \\var{b2}$$((\\var{a} \\var{op} \\var{b})\\var{op1}(\\var{a1} \\var{op2} \\var{b1}))\\var{op4}(\\var{a2} \\var{op3} \\var{b2})$
$\\var{disp[0]}$$\\var{disq[0]}$$\\var{t_value[0]}$$\\var{ev3[0]}$$\\var{final_value[0]}$
$\\var{disp[1]}$$\\var{disq[1]}$$\\var{t_value[1]}$$\\var{ev3[1]}$$\\var{final_value[1]}$
$\\var{disp[2]}$$\\var{disq[2]}$$\\var{t_value[2]}$$\\var{ev3[2]}$$\\var{final_value[2]}$
$\\var{disp[3]}$$\\var{disq[3]}$$\\var{t_value[3]}$$\\var{ev3[3]}$$\\var{final_value[3]}$
", "statement": "

In the following question you are asked to construct a truth table for:

\n

\\[((\\var{a} \\var{op} \\var{b})\\var{op1}(\\var{a1} \\var{op2} \\var{b1}))\\var{op4}(\\var{a2} \\var{op3} \\var{b2}).\\]

\n

\n

Enter T if true, else enter F.

\n

\n

\n

\n

\n

\n

\n

\n

\n

\n

\n

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Create a truth table for a logical expression of the form $((a \\operatorname{op1} b) \\operatorname{op2}(c \\operatorname{op3} d))\\operatorname{op4}(e \\operatorname{op5} f) $ where each of $a, \\;b,\\;c,\\;d,\\;e,\\;f$ can be one the Boolean variables $p,\\;q,\\;\\neg p,\\;\\neg q$ and each of $\\operatorname{op1},\\;\\operatorname{op2},\\;\\operatorname{op3},\\;\\operatorname{op4},\\;\\operatorname{op5}$ one of $\\lor,\\;\\land,\\;\\to$.

\n

For example: $((q \\lor \\neg p) \\to (p \\land \\neg q)) \\to (p \\lor q)$

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Complete the following truth table:

\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$$q$$\\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})$$\\var{a2} \\var{op3} \\var{b2}$$((\\var{a} \\var{op} \\var{b})\\var{op1}(\\var{a1} \\var{op2} \\var{b1}))\\var{op4}(\\var{a2} \\var{op3} \\var{b2})$
$\\var{disp[0]}$$\\var{disq[0]}$[[0]][[4]][[8]][[12]][[16]]
$\\var{disp[1]}$$\\var{disq[1]}$[[1]][[5]][[9]][[13]][[17]]
$\\var{disp[2]}$$\\var{disq[2]}$[[2]][[6]][[10]][[14]][[18]]
$\\var{disp[3]}$$\\var{disq[3]}$[[3]][[7]][[11]][[15]][[19]]
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