// Numbas version: exam_results_page_options {"name": "Luis's copy of Truth tables 3 (v2)-", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variables": {"ev2": {"templateType": "anything", "group": "Second Bracket", "name": "ev2", "description": "", "definition": "bool_to_label(pre_ev2)"}, "b1": {"templateType": "anything", "group": "Second Bracket", "name": "b1", "description": "", "definition": "latex(latex_symbol_list[s[3]])"}, "t_value": {"templateType": "anything", "group": "First and Second Brackets", "name": "t_value", "description": "", "definition": "bool_to_label(pre_t_value)"}, "disp": {"templateType": "anything", "group": "Truth values", "name": "disp", "description": "", "definition": "bool_to_label(p)"}, "op3": {"templateType": "anything", "group": "Third Bracket", "name": "op3", "description": "", "definition": "latex(random(\"\\\\lor\",\"\\\\land\",\"\\\\to\"))"}, "a1": {"templateType": "anything", "group": "Second Bracket", "name": "a1", "description": "", "definition": "latex(latex_symbol_list[s[2]])"}, "a2": {"templateType": "anything", "group": "Third Bracket", "name": "a2", "description": "", "definition": "latex(latex_symbol_list[s[4]])"}, "ev1": {"templateType": "anything", "group": "First Bracket", "name": "ev1", "description": "", "definition": "bool_to_label(pre_ev1)"}, "pre_t_value": {"templateType": "anything", "group": "First and Second Brackets", "name": "pre_t_value", "description": "", "definition": "map(evaluate(pre_ev1[t]+\" \"+conv(op1)+\" \"+pre_ev2[t],[]),t,0..3)"}, "disq": {"templateType": "anything", "group": "Truth values", "name": "disq", "description": "", "definition": "bool_to_label(q)"}, "final_value": {"templateType": "anything", "group": "Ungrouped variables", "name": "final_value", "description": "", "definition": "bool_to_label(map(evaluate(pre_t_value[t]+\" \"+conv(op4)+\" \"+pre_ev3[t],[]),t,0..3))"}, "ev3": {"templateType": "anything", "group": "Third Bracket", "name": "ev3", "description": "", "definition": "bool_to_label(pre_ev3)"}, "pre_ev2": {"templateType": "anything", "group": "Second Bracket", "name": "pre_ev2", "description": "", "definition": "map(evaluate(convch(a1)+\" \"+conv(op2)+\" \"+convch(b1),[p[t],q[t]]),t,0..3)"}, "pre_ev3": {"templateType": "anything", "group": "Third Bracket", "name": "pre_ev3", "description": "", "definition": "map(evaluate(convch(a2)+\" \"+conv(op3)+\" \"+convch(b2),[p[t],q[t]]),t,0..3)"}, "pre_ev1": {"templateType": "anything", "group": "First Bracket", "name": "pre_ev1", "description": "", "definition": "map(evaluate(convch(a)+\" \"+conv(op)+\" \"+convch(b),[p[t],q[t]]),t,0..3)"}, "op2": {"templateType": "anything", "group": "Second Bracket", "name": "op2", "description": "", "definition": "latex(random(\"\\\\lor\",\"\\\\land\",\"\\\\to\"))"}, "p": {"templateType": "anything", "group": "Truth values", "name": "p", "description": "", "definition": "[true,true,false,false]"}, "latex_symbol_list": {"templateType": "anything", "group": "Lists of symbols", "name": "latex_symbol_list", "description": "", "definition": "[\"p\",\"q\",\"\\\\neg p\",\"\\\\neg q\"]"}, "b2": {"templateType": "anything", "group": "Third Bracket", "name": "b2", "description": "", "definition": "latex(latex_symbol_list[s[5]])"}, "q": {"templateType": "anything", "group": "Truth values", "name": "q", "description": "", "definition": "[true,false,true,false]"}, "s": {"templateType": "anything", "group": "Lists of symbols", "name": "s", "description": "", "definition": "repeat(random(0..3),6)"}, "op4": {"templateType": "anything", "group": "Ungrouped variables", "name": "op4", "description": "", "definition": "latex(random(\"\\\\lor\",\"\\\\land\",\"\\\\to\"))"}, "op": {"templateType": "anything", "group": "First Bracket", "name": "op", "description": "", "definition": "latex(random(\"\\\\lor\",\"\\\\land\",\"\\\\to\"))"}, "logic_symbol_list": {"templateType": "anything", "group": "Lists of symbols", "name": "logic_symbol_list", "description": "", "definition": "[\"p\",\"q\",\"not p\",\"not q\"]"}, "op1": {"templateType": "anything", "group": "First and Second Brackets", "name": "op1", "description": "", "definition": "latex(random(\"\\\\lor\",\"\\\\land\",\"\\\\to\"))"}, "b": {"templateType": "anything", "group": "First Bracket", "name": "b", "description": "", "definition": "latex(latex_symbol_list[s[1]])"}, "a": {"templateType": "anything", "group": "First Bracket", "name": "a", "description": "", "definition": "latex(latex_symbol_list[s[0]])"}}, "advice": "
First we find the truth table for $\\var{a} \\var{op} \\var{b}$:
\n$p$ | $q$ | $\\var{a} \\var{op} \\var{b}$ |
---|---|---|
$\\var{disp[0]}$ | \n$\\var{disq[0]}$ | \n$\\var{ev1[0]}$ | \n
$\\var{disp[1]}$ | \n$\\var{disq[1]}$ | \n$\\var{ev1[1]}$ | \n
$\\var{disp[2]}$ | \n$\\var{disq[2]}$ | \n$\\var{ev1[2]}$ | \n
$\\var{disp[3]}$ | \n$\\var{disq[3]}$ | \n$\\var{ev1[3]}$ | \n
Then the truth table for $\\var{a1} \\var{op2} \\var{b1}$:
\n$p$ | $q$ | $\\var{a1} \\var{op2} \\var{b1}$ |
---|---|---|
$\\var{disp[0]}$ | \n$\\var{disq[0]}$ | \n$\\var{ev2[0]}$ | \n
$\\var{disp[1]}$ | \n$\\var{disq[1]}$ | \n$\\var{ev2[1]}$ | \n
$\\var{disp[2]}$ | \n$\\var{disq[2]}$ | \n$\\var{ev2[2]}$ | \n
$\\var{disp[3]}$ | \n$\\var{disq[3]}$ | \n$\\var{ev2[3]}$ | \n
Putting these together to find $(\\var{a} \\var{op} \\var{b})\\var{op1}(\\var{a1} \\var{op2} \\var{b1})$:
\n\n$p$ | $q$ | $\\var{a} \\var{op} \\var{b}$ | $\\var{a1} \\var{op2} \\var{b1}$ | $(\\var{a} \\var{op} \\var{b})\\var{op1}(\\var{a1} \\var{op2} \\var{b1})$ |
---|---|---|---|---|
$\\var{disp[0]}$ | \n$\\var{disq[0]}$ | \n$\\var{ev1[0]}$ | \n$\\var{ev2[0]}$ | \n$\\var{t_value[0]}$ | \n
$\\var{disp[1]}$ | \n$\\var{disq[1]}$ | \n$\\var{ev1[1]}$ | \n$\\var{ev2[1]}$ | \n$\\var{t_value[1]}$ | \n
$\\var{disp[2]}$ | \n$\\var{disq[2]}$ | \n$\\var{ev1[2]}$ | \n$\\var{ev2[2]}$ | \n$\\var{t_value[2]}$ | \n
$\\var{disp[3]}$ | \n$\\var{disq[3]}$ | \n$\\var{ev1[3]}$ | \n$\\var{ev2[3]}$ | \n$\\var{t_value[3]}$ | \n
Next we find the truth table for $\\var{a2} \\var{op3} \\var{b2}$:
\n$p$ | $q$ | $\\var{a2} \\var{op3} \\var{b2}$ |
---|---|---|
$\\var{disp[0]}$ | \n$\\var{disq[0]}$ | \n$\\var{ev3[0]}$ | \n
$\\var{disp[1]}$ | \n$\\var{disq[1]}$ | \n$\\var{ev3[1]}$ | \n
$\\var{disp[2]}$ | \n$\\var{disq[2]}$ | \n$\\var{ev3[2]}$ | \n
$\\var{disp[3]}$ | \n$\\var{disq[3]}$ | \n$\\var{ev3[3]}$ | \n
Putting this all together to obtain the truth table we want:
\n$p$ | $q$ | $(\\var{a} \\var{op} \\var{b})\\var{op1}(\\var{a1} \\var{op2} \\var{b1})$ | $\\var{a2} \\var{op3} \\var{b2}$ | $((\\var{a} \\var{op} \\var{b})\\var{op1}(\\var{a1} \\var{op2} \\var{b1}))\\var{op4}(\\var{a2} \\var{op3} \\var{b2})$ |
---|---|---|---|---|
$\\var{disp[0]}$ | \n$\\var{disq[0]}$ | \n$\\var{t_value[0]}$ | \n$\\var{ev3[0]}$ | \n$\\var{final_value[0]}$ | \n
$\\var{disp[1]}$ | \n$\\var{disq[1]}$ | \n$\\var{t_value[1]}$ | \n$\\var{ev3[1]}$ | \n$\\var{final_value[1]}$ | \n
$\\var{disp[2]}$ | \n$\\var{disq[2]}$ | \n$\\var{t_value[2]}$ | \n$\\var{ev3[2]}$ | \n$\\var{final_value[2]}$ | \n
$\\var{disp[3]}$ | \n$\\var{disq[3]}$ | \n$\\var{t_value[3]}$ | \n$\\var{ev3[3]}$ | \n$\\var{final_value[3]}$ | \n
Complete the following truth table:
\n$p$ | $q$ | $\\var{a} \\var{op} \\var{b}$ | $\\var{a1} \\var{op2} \\var{b1}$ | $(\\var{a} \\var{op} \\var{b}) \\var{op1} (\\var{a1} \\var{op2} \\var{b1})$ | $\\var{a2} \\var{op3} \\var{b2}$ | $((\\var{a} \\var{op} \\var{b})\\var{op1}(\\var{a1} \\var{op2} \\var{b1}))\\var{op4}(\\var{a2} \\var{op3} \\var{b2})$ |
---|---|---|---|---|---|---|
$\\var{disp[0]}$ | \n$\\var{disq[0]}$ | \n[[0]] | \n[[4]] | \n[[8]] | \n[[12]] | \n[[16]] | \n
$\\var{disp[1]}$ | \n$\\var{disq[1]}$ | \n[[1]] | \n[[5]] | \n[[9]] | \n[[13]] | \n[[17]] | \n
$\\var{disp[2]}$ | \n$\\var{disq[2]}$ | \n[[2]] | \n[[6]] | \n[[10]] | \n[[14]] | \n[[18]] | \n
$\\var{disp[3]}$ | \n$\\var{disq[3]}$ | \n[[3]] | \n[[7]] | \n[[11]] | \n[[15]] | \n[[19]] | \n
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\nEnter T if true, else enter F.
\n\n\n\n\n\n\n\n\n\n\n", "metadata": {"notes": "", "description": "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 $\\lor,\\;\\land,\\;\\to$.
\nFor example: $((q \\lor \\neg p) \\to (p \\land \\neg q)) \\to (p \\lor q)$
", "licence": "Creative Commons Attribution 4.0 International"}, "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/"}]}