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# Consider the function α : Q → Q defined by the formula?

Consider the function α : Q → Q defined by the formula

α(x) = 4x. Demonstrate that α does not posess the homomorphism property for the set Q with the binary operation multiplication (Q, ·), i.e., you

must show that

α(xy) 6 not = α(x) · α(y)

### 1 Answer

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- Iggy RockoLv 74 weeks ago
Just two rational numbers that form a counterexample.

Let x = 1 and y = 1.

α(1 * 1) = a(1) = 4(1) = 4

α(1) * α(1) = 4(1) * 4(1) = 4 * 4 = 16

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