Sets, Relations & Functions
Logic and Statements
Grade 11
Question:
<p>Suppose \(p\): A natural number \(n\) is odd and \(q\): natural number \(n\) is not divisible by 2, then the biconditional statement \(p \Leftrightarrow q\) is</p>
<p>(a) A natural number \(n\) is odd, if and only if it is divisible by 2</p>
<p>(b) A natural number \(n\) is odd, if and only if it is not divisible by 2</p>
Step-by-Step Solution
Key Concept: A biconditional statement \(p \Leftrightarrow q\) combines 'if p then q' and 'if q then p'.
<p>The biconditional statement \(p \Leftrightarrow q\) reads as '\(p\) if and only if \(q\)'.</p><p>Given: \(p\) is 'A natural number \(n\) is odd' and \(q\) is 'natural number \(n\) is not divisible by 2'.</p><p>Therefore, \(p \Leftrightarrow q\) is: 'A natural number \(n\) is odd, if and only if it is not divisible by 2'.</p><p>∴ Answer is (b).</p>
Correct Answer: B