For all numbers X and Y, let the operation â˜¼ be defined by X â˜¼ Y=XY-Y. If M and N are positive integers

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For all numbers X and Y, let the operation â˜¼ be defined by X â˜¼ Y=XY-Y. If M and N are positive integers

[From: ] [author: ] [Date: 13-01-21] [Hit: ]

M â˜¼ (M+N)-Note that M â˜¼ N = MN - N = N(M - 1) = 0 whenever M = 1.Next, (M+N) â˜¼ N = (M+N)N - N = N((M+N) - 1) = 0 only when M + N = 1, which can not occur since we need both M, N > 0.Finally,......

Which of the following can be equal to zero?
I. M â˜¼ N
II. (M+N) â˜¼ N
III. M â˜¼ (M+N)

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Note that M â˜¼ N = MN - N = N(M - 1) = 0 whenever M = 1.

Next, (M+N) â˜¼ N = (M+N)N - N = N((M+N) - 1) = 0 only when M + N = 1, which can not occur since we need both M, N > 0.

Finally, M â˜¼ (M+N) = M(M+N) - (M+N) = (M+N)(M - 1) = 0 whenever M = 1.

So, both I and III are the answers.

I hope this helps!

1

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