Consider the statements: p it is hot, q: it is raining Which of the following symbols correctly represents the…

Analyze the question

We are given:

• p: it is hot
• q: it is raining

The statement is "It is raining if and only if it is cold."

Explain the concept

• "If and only if" is the biconditional symbol ⟺.
• "Cold" is taken as the opposite of "hot", so "it is cold" is written as ~p (not hot).

Solve step by step

1. "It is raining" is q.
2. "It is cold" is ~p.
3. Joining them with "if and only if": q ⟺ ~p

Check the options

• A. p ⟺ ~q means "hot iff not raining". This is not the statement.
• B. p ⟺ q means "hot iff raining". This is not the statement.
• C. ~p ⟺ ~q means "cold iff not raining". This is not the statement.
• D. q ⟺ ~p means "raining iff cold". This matches the statement.

Answer: D

Tip: In logic questions, first write each part of the sentence as a symbol (here, "raining" = q and "cold" = ~p). Then join the parts with the connective. Watch the order of the clauses: the first clause in the sentence should come first in the symbols. Also remember that "cold" is treated as "not hot" in these problems.