Consider the statement :
“For an integer n, if \(n^3 - 1\) is even, then n is odd.”
The contrapositive statement of this statement is :
“For an integer n, if \(n^3 - 1\) is even, then n is odd.”
The contrapositive statement of this statement is :
Show Hint
- For an integer n, if n is even, then \(n^3 - 1\) is even.
- For an integer n, if \(n^3 - 1\) is not even, then n is not odd.
- For an integer n, if n is odd, then \(n^3 - 1\) is even.
- For an integer n, if n is even, then \(n^3 - 1\) is odd.
The Correct Option is D
Solution and Explanation
Its contrapositive is \(\sim q \Rightarrow \sim p\).
\(\sim q\): n is not odd, i.e. n is even. \(\sim p\): \(n^3 - 1\) is not even, i.e. \(n^3 - 1\) is odd.
So the contrapositive is: “For an integer n, if n is even, then \(n^3 - 1\) is odd.”
(Option 2 is the inverse \(\sim p \Rightarrow \sim q\) and option 3 is the converse \(q \Rightarrow p\).)
Answer: (4) For an integer n, if n is even, then \(n^3 - 1\) is odd.
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