GO Classes CS 2025 | Weekly Quiz 3 | Propositional Logic | Question: 2

Answer 1

A row in a truth table is known as Intrepretation. (An Intrpretation is a combination of truth values assigned to the propositional variables)

One of the given intrepretation $v$ is $p = F, q = T, r = T$

Option A: $(p \rightarrow \sim q) \vee \sim(r \wedge q) = T$

Option B: $(\sim p \vee \sim q) \rightarrow (p \vee \sim r) = F$

Option C: $\sim(\sim p \rightarrow \sim q) \wedge r = T$

Option D: $\sim(\sim p \rightarrow (q \wedge \sim r )) = T$

Option A, C, D True and hence are said to satisfy the given intrepretation $v$

Answer 2

An interpretation of formula $Z$, in propositional logic, is truth assignment to all the propositional variables of $Z$. An interpretation $I$ satisfies $Z$ if and only if $Z$ is true in $I$. $v$ satisfies $A, C$ and $D$. $v$ does not satisfy $B$.

v(p) = F means that in the interpretation v, the truth value of p = F.

Likewise, v(p) = T will mean that in the interpretation v, the truth value of p = T.

Learn Interpretation & Model in Propositional Logic: https://www.youtube.com/watch?v=12lUdO2mOp4 

Detailed Video Solution: Interpretation in Propositional Logic 

Answer 3

Satisfied by v simply means which of them is valid and valid means tautology.

Upon solving all the options, A,C,D are tatutologies hence the answer.