Help with discrete math question. Show the following Statement is true: Let n be an integer. If 5n+2 is odd, then n is odd.?

This is a proof by contrapositive.

2 Answers

  • ?
    Lv 7
    3 years ago
    Favourite answer

    The contrapositive here is "If n is not odd, then 5n+2 is not odd."

    If n is not odd, it is even; n = 2k, where k is some integer.

    Then 5n+2 = 5(2k) + 2 = 10k + 2 = 2(5k+1). This is a multiple of 2, so 5n+2 is even. QED.

  • 3 years ago

    Statement: If 5n + 2 is odd, then n is odd.

    Contrapositive: If n is even, then 5n + 2 is even.

    If a statement is true, its contrapositive is true, and vice versa.

    If n is even, then multiplying is by any integer will produce an even number.

    If an even number (like 2) is added to an even number, the result is an even number.

    Thus: if n is even, then (even number [5n]) + (even number [2]) = even number.

    Contrapositive proven true.

    Statement proven true.

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