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Let m be an integer. Use contraposition to show that if m² is not divisible by 5 , then m is not divisible by 5

User Pengwang
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Final answer:

To use contraposition to prove that if m² is not divisible by 5, then m is not divisible by 5, we show the contrapositive: if m is divisible by 5, then m² is divisible by 5 since m²=(5k)² for some integer k is clearly divisible by 5.

Step-by-step explanation:

To show that if m² is not divisible by 5, then m is not divisible by 5 using contraposition, we begin by considering the contrapositive of the given statement. The contrapositive of 'if m² is not divisible by 5, then m is not divisible by 5' is 'if m is divisible by 5, then m² is divisible by 5.' This statement is true because if m is divisible by 5, then m can be written as 5k for some integer k. Hence, m² = (5k)² = 25k², which is clearly divisible by 5 since it is a multiple of 5. Therefore, by contraposition, if m² is not divisible by 5, m must also not be divisible by 5.

User Federico Piragua
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