Question

The contrapositive of the statement “if \(2^2 = 5\), then I got first class” is

• A. If I do not get a first class, then \(2^2 = 5\)
• B. If I do not get a first class, then \(2^2 \neq 5\)
• C. If I get a first class, then \(2^2 = 5\)
• D. If I get a first class, then \(2^2 \neq 5\)

Hint:

For any statement: \[ P \Rightarrow Q \]
Contrapositive: \(\neg Q \Rightarrow \neg P\)
A statement and its contrapositive are always \textbf{logically equivalent}

Answer 1

The Correct Option is B

Step 1: Write the given statement in logical form. Let \[ P:\; 2^2 = 5, \qquad Q:\; \text{I got first class} \] The given statement is: \[ P \Rightarrow Q \]
Step 2: The contrapositive of a statement \(P \Rightarrow Q\) is: \[ \neg Q \Rightarrow \neg P \]
Step 3: Negate the statements: \[ \neg Q:\; \text{I do not get a first class} \] \[ \neg P:\; 2^2 \neq 5 \]
Step 4: Hence, the contrapositive is: \[ \text{If I do not get a first class, then } 2^2 \neq 5 \]