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A. K ARULMOZHI

4 years

Mathematics

University

Rules of Inference

A. K ARULMOZHI

272
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10 questions

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1. Multiple Choice
30 seconds
1 pt
$p\rightarrow q,\ p\ \$ implies $q$ also written $\left(p\rightarrow q\right)\wedge p\Longrightarrow q$
Modus Ponnens
Modus Tollens
Disjunctive Syllogism
Hypothetical Syllogism
2. Multiple Choice
30 seconds
1 pt
$\left(p\rightarrow q\right),\ \sim q\$ implies $\sim p$
Modus Ponens
Modus Tollens
Disjunctive Syllogism
Simplification
3. Multiple Choice
30 seconds
1 pt
$\left(p\rightarrow q\right),\ \left(q\rightarrow r\right)\$ implies $\left(p\rightarrow r\right)$
Modus Ponens
Modus Tollens
Distributive Syllogism
Hypothetical Syllogism
4. Multiple Choice
30 seconds
1 pt
$\left(p\vee q\right),\ \sim p$ implies $q$
Modus Ponens
Disjunctive Syllogism
Simplification
Addition
5. Multiple Choice
30 seconds
1 pt
"If A works hard, then either B or C will enjoy themselves". " If B enjoys himself then A will not work hard".
"If D enjoys himself, then C will not".
Therefore, " if A works hard, D will not enjoy himself". Formulate these sentences
$A\rightarrow\left(B\wedge C\right),\ B\longrightarrow A,\ D\longrightarrow C$ $Therefore\ A\ \rightarrow D$
$A\rightarrow\left(B\vee C\right),\ B\longrightarrow\sim A,\ D\longrightarrow\sim C\$ $Therefore\ \ A\rightarrow\sim D$
None of the above
6. Multiple Choice
30 seconds
1 pt
$p\vee q\Longleftrightarrow q\vee p\$ and $p\wedge q\Longleftrightarrow q\wedge p$
Commutative laws
De Morgan’s laws
Idempotent laws
Absorption law
7. Multiple Choice
30 seconds
1 pt
$p\vee p\Longleftrightarrow p$ and $p\wedge p\Longleftrightarrow p$
De Morgan’s laws
modus ponens
Associative laws
Idempotent laws
8. Multiple Choice
30 seconds
1 pt
which one of the following is an absorption law?
$p\wedge\left(p\vee q\right)\Longleftrightarrow p$ and $p\vee\left(p\wedge q\right)\Longleftrightarrow p$
$p\wedge p\Longleftrightarrow p$ and $p\vee p\Longleftrightarrow p$
$p\wedge q\Longleftrightarrow q\wedge p$ and $p\vee q\Longleftrightarrow q\vee p$
$p\vee\left(q\vee r\right)\Longleftrightarrow\left(p\vee q\right)\vee r$ and $p\wedge\left(q\wedge r\right)\Longleftrightarrow\left(p\wedge q\right)\wedge r$
9. Multiple Choice
30 seconds
1 pt
$\sim\left(p\vee q\right)\Longleftrightarrow\sim p\wedge\sim q$ and $\sim\left(p\wedge q\right)\Longleftrightarrow\sim p\vee\sim q$
Distributive laws
Associative laws
De Morgan’s laws
Absorption law
10. Multiple Choice
30 seconds
1 pt
$p\wedge\left(q\vee r\right)\Longleftrightarrow\left(p\wedge q\right)\vee\left(p\wedge r\right)$ and $p\vee\left(q\wedge r\right)\Longleftrightarrow\left(p\vee q\right)\wedge\left(p\vee r\right)$
Associative laws
Distributive laws
Absorption law
none of the above
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