KCET · Maths · Mathematical Reasoning
The contrapositive of the converse of the statement "If \( x \) is a prime number then \( x \) is odd" is
- A If \( x \) is not a prime number then \( x \) is odd.
- B If \( x \) is not an odd number then \( x \) is not a prime number.
- C If \( x \) is a prime number then it is not odd.
- D If \( x \) is not a prime number then \( x \) is not an odd.
Answer & Solution
Correct Answer
(D) If \( x \) is not a prime number then \( x \) is not an odd.
Step-by-step Solution
Detailed explanation
Let \(p: x\) is a prime number and \(q: x\) is an odd number.
So, \(p \rightarrow q\)
and converse, \(q \rightarrow p\)
Now, contrapositive is \(\sim p \rightarrow \sim q\)
Therefore, if \(x\) is not a prime number then \(x\) is not odd number.
So, \(p \rightarrow q\)
and converse, \(q \rightarrow p\)
Now, contrapositive is \(\sim p \rightarrow \sim q\)
Therefore, if \(x\) is not a prime number then \(x\) is not odd number.
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