Question

Find the truth value of the statement: "If 2 is even, then 5 is prime."

• A. True
• B. False
• C. Cannot be determined
• D. None of these

Hint:

An implication is false only when a true statement leads to a false statement. Otherwise, it is always true.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks for the truth value of a conditional statement (implication) in Mathematical Logic.
Step 2: Key Formula or Approach:
The statement is of the form "If \( p \), then \( q \)" (\( p \to q \)).
The truth table for \( p \to q \) is False only when \( p \) is True and \( q \) is False.
Step 3: Detailed Explanation:
Let \( p \): "2 is even" and \( q \): "5 is prime".
Evaluating individual statements:
\( p \) is a True statement (T).
\( q \) is a True statement (T).
The conditional statement is \( T \to T \).
From the logic truth table, \( T \to T = T \).
Step 4: Final Answer:
The truth value of the overall statement is True.