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.

B.

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

A. 2n– 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. 2n– 1 is always even: Once again, 2n will always be even. So 2n-1 will always be odd. This conjecture is false.

C. 2n– 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. 2n– 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.