GO Classes CS 2025 | Weekly Quiz 1 | Propositional Logic | Question: 2

Answer 1

Let, $p:$ $a^2 + b^2 = c^2$ and $q:$ triangle T be a right triangle.

Given: “A sufficient condition for $q$ is $p$” which is same as “If $p$ then $q$” i.e. $p\rightarrow q$

• A. “If $q$ then $p$” i.e. “$q\rightarrow p$” which is not equivalent to the given statement (we can not comment).
• B. “If $p$ then $q$” which is equivalent to the given statement, hence Correct.
• C. “If $\sim p$ then $\sim q$” which is the inverse of the given statement hence it is also not equivalent.
• D. “$q$ only if $p$” means $p$ is necessary for $q$ i.e. “$q\rightarrow p$” which is also not equivalent to the given statement.

Therefore, $\textbf{B}$ is the correct option.

Answer 2

$p\rightarrow q$ means $p$ is sufficient condition for q.

Detailed Video Solution is here: Weekly Quiz 4 Solutions

Answer 3

Here P : a^2+b^2=c^2     Q : Triangle T be a right triangle

Here the statement in the question is implying to if then q means p -→ q so the below options which satisfies is the answer.

• A. False as it implies q -→ p
• B. True as here it is if q then p so its same as p -→ q
• C. False as it implies if ~p then q which is not same as p -→ q
• D. False as it implies q only if p, which is not same as p -→ q

So the correct Option is (B)

Answer 4

A.p->q

C.not q-> not p

D.p->q

So a,c,d are correct