If A B C can we say that B C A Why Prove if this is true

If A & B = C, can we say that B & C = A? Why? Prove if this is true or provide a example if this is false. If A|B = C, can we say that B | C = A? Why? Prove if this is true or provide an example if this is false.

Solution

a) if A&B = C, then B&C=A is NOT TRUE.

Example: A = 1, B = 0 => A&B = 1&0 = 0 = C, Then B&C = 0&0 = 0 != A

b)

if A|B = C, then B|C=A is NOT TRUE.

Example: A = 0, B = 1 => A|B = 1|0 = 1 = C, Then B|C = 1&1 = 1 != A