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Are f and g both necessarily onto, if `gof`is onto? |
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Answer» Let `f: A->B` and `g:B->C` are two functions such that `gof: A->C` We are given `gof` is onto. Let `A = {a_1,a_2,a_3}` Let `C = {c_1,c_2,c_3}` As `gof` is onto there will be mapping between each elements of set `C` with every element of set `A`. Now, Let `B = {b_1,b_2,b_3,b_4}` As set `B` contains more elements than `A` and `C` so it will not have mapping of its all elements with elements of set `A` and set `C`. That means it is not neccesary that `f` and `g` are also onto function. |
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