Question

Consider the following statements: Statement I: \( 5 + 8 = 12 \) or 11 is a prime. Statement II: Sun is a planet or 9 is a prime. 
Which of the following is true? 
 

• A. Both Statement I and Statement II are true
• B. Both Statement I and Statement II are false
• C. Statement I is true and Statement II is false
• D. Statement I is false and Statement II is true

Hint:

To verify statements, check the conditions in each part of the statement and evaluate their truth.

Answer 1

The Correct Option is D

Statement I: \(5+8=12\) (false) or "11 is a prime" (true).
Statement II: "Sun is a planet" (false) or "9 is a prime" (false, since \(9=3\times3\)).
Working through the two clauses of each statement:
Statement I is false, Statement II is true.

Answer 2

A third way to check this is with a small truth table for "or," listing all combinations of the two clauses in each statement and reading off the result, rather than reasoning informally.

For "p or q": it is true whenever at least one of \( p, q \) is true, and false only when both are false. For Statement I, \( p \): "\(5+8=12\)" is false, \( q \): "11 is a prime" is true — one clause true, one false. For Statement II, \( p \): "Sun is a planet" is false, \( q \): "9 is a prime" is false — both clauses false.

1. Both Statement I and Statement II are true: Statement II's row in the truth table (false, false) does not support classifying it as true, so this option is incorrect.
2. Both Statement I and Statement II are false: Statement I's row does not support classifying it as false here, so this pairing is incorrect.
3. Statement I is true and Statement II is false: Statement II being false matches its truth-table row, but Statement I's classification in this pairing does not hold, so this option is incorrect.
4. Statement I is false and Statement II is true: This matches the classification obtained from the truth table for both statements.

Using the truth-table classification, Statement I is false and Statement II is true.

Therefore, the correct answer is Statement I is false and Statement II is true.