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Write the contra positive of the followi...

Write the contra positive of the following statements:
(a) If 5 > 7 then 6 > 7.
(b) x is even number implies that x2 is divisible by 4.

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The correct Answer is:
To find the contrapositive of a statement of the form "If P then Q," we need to reverse the implication and negate both the hypothesis (P) and the conclusion (Q). The contrapositive can be expressed as "If not Q then not P." Let's apply this to the given statements: ### (a) Statement: If 5 > 7 then 6 > 7. 1. **Identify P and Q**: - P: 5 > 7 - Q: 6 > 7 2. **Negate Q and P**: - Not Q: 6 ≤ 7 (which means 6 is not greater than 7) - Not P: 5 ≤ 7 (which means 5 is not greater than 7) 3. **Write the contrapositive**: - The contrapositive will be: If 6 ≤ 7, then 5 ≤ 7. ### (b) Statement: x is an even number implies that x² is divisible by 4. 1. **Identify P and Q**: - P: x is an even number - Q: x² is divisible by 4 2. **Negate Q and P**: - Not Q: x² is not divisible by 4 - Not P: x is not an even number (which means x is an odd number) 3. **Write the contrapositive**: - The contrapositive will be: If x² is not divisible by 4, then x is not an even number. ### Final Answers: (a) If 6 ≤ 7, then 5 ≤ 7. (b) If x² is not divisible by 4, then x is not an even number. ---
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