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Statement - 1 : For each natural number n, (n+1)^7 - n^7 is divisible by 7. Statement - 2 : For each natural number n, n^7 - n is divisible by 7.

1. Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1
2. Statement-1 is true, Statement-2 is true; Statement-2 is NOT a correct explanation for Statement-1
3. Statement-1 is true, Statement-2 is false
4. Statement-1 is false, Statement-2 is true

Correct answer: Statement-1 is true, Statement-2 is false

Solution

Statement-1 is true because it can be shown using the binomial theorem that the difference (n+1)^7 - n^7 is divisible by 7 for all natural numbers n. However, Statement-2 is false because not all natural numbers n satisfy the condition that n^7 - n is divisible by 7, as demonstrated by counterexamples.

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