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Suppose f:A to B " and " B to C. (i) P...

Suppose `f:A to B " and " B to C.`
(i) Prove that if `f` is onto and g is not one-one, then `gof` is not one-to-one
(ii) Prove that if `f` is not and g is one-one, then `gof` is not onto.

Text Solution

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Let `z in D,` then there is some `y in C` such that `g(y)=z`
` :.` Now if `y notin B`, then there is no x for which `f(x)=y`
` :. gof` is not onto.
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