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28 September, 07:57

If n is an integer, which conjecture is not true about 2n - 1? A. 2n - 1 is odd if n is positive. B. 2n - 1 is always even. C. 2n - 1 is odd if n is even. D. 2n - 1 is always odd.

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  1. 28 September, 08:16
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    B.

    Let's simply look at each conjecture and determine if it's true or false.

    A. 2nâ€" 1 is odd if n is positive: Since n is an integer, 2n will always be even. And an even number minus 1 is always odd. Doesn't matter if n is positive or not. So this conjecture is true.

    B. 2nâ€" 1 is always even: Once again, 2n will always be even. So 2n-1 will always be odd. This conjecture is false.

    C. 2nâ€" 1 is odd if n is even: 2n is always even, so 2n-1 will always be odd, regardless of what n is. So this conjecture is true.

    D. 2nâ€" 1 is always odd: 2n will always be even. So 2n-1 will always be odd. Once again, this conjecture is true.

    Of the 4 conjectures above, only conjecture B is false. So the answer is B.
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