Immediate Help Required in discrete mathematics
I am stuck in this below problems. Please help.
1. Prove that if H, K are subgroups of a group G and H Ų K = G. Then either H=G or K=G
2. Let G be a group and a, b Є G. Then the equation x*a=b has a unique solution given by x= b* a
3. Linear sum W1+ W2 of two subspaces W1and W2 of a vector spaceV(F) is A subspace of V(F)
4. show that the function T: R2 → R2 such that T(0,1)=(3,4),T(3,1)=(2,2) And T(3,2)=(5,7) is not a L.T.
5. Let T:v →w be a linear transformation. Then T is onto iff p(T)= dim w.
6. show that the function T: R2 → R2 defined by T(x1,x2)=(x1-x2,x1+x2),for (x1,x2)Є R2 is bijective.
