Let f : G → H be a homomorphism with kernel K. Show (a) K is a subgroup of G.(b) For any y ∈ H, f−1(y), the preimage of y, is a left coset of K.

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Q: 5. Consider the group (R+, 0). Prove that the function F: R -R given by: F (x.y) = (x +y.r-y) is a…

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Q: 2. Let H and K be subgroups of the group G. (a) For x, y E G, define x ~ y if x = hyk for some h e H…

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