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January 29th, 2018, 11:02 PM   #1
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Why is choice 3 the answer?

(ex) Which of the following statements is true?

(1) If P=Q, then P^n=Q^n where n is any integer
(2) If P^n=Q^n, then P=Q where n is any integer
(3) If P=Q, then P^n=Q^n where n is any positive integer
(4) If P^n=Q^n, then P=Q where n is any positive integer

my attempt

If I let P and Q be 2 and let n be 1, these values satisfy all four choices.

Next, I let P and Q be 2 and let n be -1. these values satisfy (1) and (2).

So, I don't know why the answer key says (3) is the answer. Please help me. Thanks a lot.
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January 29th, 2018, 11:58 PM   #2
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you can't prove anything by finding an example that works, you can only disprove something by finding an example that doesn't.

(1) would be true except that 1/0 is undefined so that the statement isn't true when P=Q=0 when n is negative

(2) isn't true for Q=-P and n even

(3) is true

(4) is false for the same reason as (2)
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January 30th, 2018, 11:49 PM   #3
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Thank you very much again, romsek.
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