DGD7

(1) Give a rigorous proof that A intersect B = A if and only if A-B is the empty set.



(2) Injective/surjective functions: review the definitions of a function, injective (one-to-one) function, surjective (onto) function

 SE 5: #1abd, #9b, #5de



(3) Bijections/invertible functions: review the definition of a bijection, inverse function, invertible function

(a) Is f: R -> R, defined by f(x)=2x^3-5, invertible? If so, find its inverse. What if the domain and co-domain were Z instead?

(b) Is f: Q^2 -> Q^2 defined by f(x,y)=(x+y,x-y) invertible? If so, find its inverse.