Let A, B, and C be subsets of a universal setU. Prove the following set identity A(BC)AC= A(C B)in two ways: 1)using a membership table (with a brief...

Let A, B, and C be subsets of a universal setU. Prove the following set identity A∪(B⊕C)−A∩C= A∪(C ∩B)in two ways:

1)using a membership table (with a brief explanation).

2)using the laws in the Table of Important Set Identities (see page 2 in LEC 11 notes). Useexactlyonelawperstepandwritethenameofthelawusedbesideeachstep. Be very careful that you do not omit necessary parentheses. Start with the left set (LS) and apply the laws (one at a time) until your expression equals the right set (RS). LS =A∪(B⊕C)−A∩C =?