// Numbas version: finer_feedback_settings {"name": "ma219_Logikk", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {"convch": {"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]\")", "type": "string", "parameters": [["ch", "string"]], "language": "jme"}, "list_to_boolean": {"definition": "map(if(l[x]<>0,true,false),x,0..length(l)-1)", "type": "list", "parameters": [["l", "list"]], "language": "jme"}, "conv": {"definition": "switch(op=\"\\\\land\",\"and\",op=\"\\\\lor\",\"or\",\"implies\")", "type": "string", "parameters": [["op", "string"]], "language": "jme"}, "evaluate": {"definition": "return scope.evaluate(expr);", "type": "number", "parameters": [["expr", "string"], ["dependencies", "list"]], "language": "javascript"}, "cart": {"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))", "type": "number", "parameters": [["n", "number"]], "language": "jme"}, "bool_to_label": {"definition": "map(if(l[x],'S','F'),x,0..length(l)-1)", "type": "number", "parameters": [["l", "list"]], "language": "jme"}}, "ungrouped_variables": ["pre_final_value", "op4", "logic_values", "final_value"], "name": "ma219_Logikk", "tags": [], "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\n\n\n\n\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

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\n\n\n\n\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]}$
\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\n\n\n\n\n\n\n\n\n\n\n\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]}$
\n

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

\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\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

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\n\n\n\n\n\n \n\n\n\n\n\n\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]}$
", "rulesets": {}, "parts": [{"prompt": "

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\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]}$$\\var{r[3]}$[[3]]
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$\\var{p[5]}$$\\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]]
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Fyll ut sannhetstabellen for det logiske uttrykket: \\[((\\var{a} \\var{op} \\var{b})\\var{op1}(\\var{a1} \\var{op2} \\var{b1}))\\var{op4}\\var{a2}\\] Tast inn S for sann og F for falsk.

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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 $ where each of $a, \\;b,\\;c,\\;d,\\;e$ can be one the Boolean variables $p,\\;q,\\;r,\\;\\neg p,\\;\\neg q,\\;\\neg r$ and each of $\\operatorname{op1},\\;\\operatorname{op2},\\;\\operatorname{op3},\\;\\operatorname{op4}$ one of $\\lor,\\;\\land,\\;\\to$.

\n

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

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