Question

Hello, this is for Discrete Math. I really need help with the problem below. I promise to thumbs up for solid answers. Thank you very much!

4 (8 points) Use an element argument to prove that for all sets A and B if ASB , th

Answer 1

A is subset of B

which means

x in A =>(then) x in B

which is identical to

x not in B =>(then) x not in A

x in complement of B =>(then)
x in complement of A

So

B' subset of A'

where ' means complement.

Theoreim: If ACB, then BCCA Proof: Let ACB. then if xEA then xEB The contrapositive of the above is if x¢B, then x£4 This is equivalent to if xEBC, then xEA That is the definition of BAS.