GATE CSE 2024 | Set 2 | Question: 2

Question

​​​​Let $p$ and $q$ be the following propositions:

$p$ : Fail grade can be given.
$q$ : Student scores more than $50 \%$ marks.

Consider the statement: "Fail grade cannot be given when student scores more than $50 \%$ marks."

Which one of the following is the CORRECT representation of the above statement in propositional logic?

• A.  $q \rightarrow \neg p$
• B.  $q \rightarrow p$
• C.  $p \rightarrow q$
• D.  $\neg p \rightarrow q$

Comments

answer is 

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$P$ when $Q$ mean $Q$ implies $P$(Q $\longrightarrow$P)

$P$: Fail grade can be given

$Q$: Student scores more than $\mathbf{5 0} \%$ Marks

~ P: Fail grade can not be given

Hence, $Q$----->~ P (option A)

Answer 1

Q when P means P→Q.
Given statement,

P: Fail grade can be given.
Q: Student score more than 50% marks.
¬P : Fail grade cannot be given
So,
Fail grade cannot be given when student score more than 50% marks.
is written as  Q→¬P

Correct answer is option A.
 

Answer 2

A: q -> ~p

Answer 3

$P$ when $Q$ mean $Q$ implies $P$(Q $\longrightarrow$P)

$P$: Fail grade can be given

$Q$: Student scores more than $\mathbf{5 0} \%$ Marks

~ P: Fail grade can not be given

Hence, $Q$----->~ P (option A)