GATE CSE 2026 | Set 2 | GA | Question: 5

Question

'When it is raining, peacocks dance.'

Based only on this sentence, which one of the following options is necessarily true?

• A. Peacocks dance only when it is raining.
• B. When peacocks dance, it is raining.
• C. When peacocks are not dancing, it is not raining.
• D. When it is not raining, peacocks do not dance.

Comments

By using the property of contrapositve i. e.
P-->Q     is TRUE
negationQ---->negationP    is also TRUE
So

p = peacocks dance
q = when it is raining
then
when peacoks are not dancing , it is not raining
Option C is correct

Answer 1

Let P and Q be two statements such that:

P: It is raining.

Q: Peacocks Dance.

Converting given statement in terms of P and Q provides:

$$P \implies Q$$

$$\because P \implies Q \equiv \neg Q \implies \neg P $$

$ \neg Q \implies \neg P \equiv$ "When peacocks are not dancing, it is not raining".

Hence, Option C is the correct answer.

Answer 2

P --> R
R' --> P'

Answer 3

The given sentence "When it is raining, peacocks dance" can be written as $P → Q$ (If $P,$ then $Q$). In logic, a conditional statement is logically equivalent to its contrapositive, which is $¬Q → ¬P$ (If not $Q,$ then not $P$). 

• $P → Q: $ If it is raining, then peacocks dance.
• $¬Q → ¬P:$ If peacocks are not dancing, then it is not raining. 

Since the contrapositive is always true if the original statement is true, "When peacocks are not dancing, it is not raining" is the only option that is necessarily true based solely on the information provided. 

Answer 4

C

 

Answer 5

P = It is raining

Q = Peacocks dance

So the statement is:

                                       P→Q

 

Now remember an important logic rule:

                               P→Q  ≡  ¬Q→¬P    

This is called the contrapositive (necessarily true).

 

So:

If peacocks are not dancing→it is not raining

which matches:

✅ Option C: “When peacocks are not dancing, it is not raining.”

---

 

Why others are wrong:

• A: “Peacocks dance only when it is raining.”
  Means Q→P (reverse statement) — not guaranteed.

 

• B: “When peacocks dance, it is raining.”
  Again Q→P  — not necessarily true.

 

• D: “When it is not raining, peacocks do not dance.”
  Also ¬P→¬Q — inverse statement, not guaranteed.

Answer 6

When it is not raining, peacocks do not dance