If A is a subset of B, prove that (C\\B) is a subset of (C\\A). Given A is not e
ID: 1942592 • Letter: I
Question
If A is a subset of B, prove that (CB) is a subset of (CA). Given A is not equal to B. Either prove the converse is true or give a counterexample.Explanation / Answer
Note that x in A ==> x in B is equivalent to its contrapositive x not in B ==> x not in A. (1) If x is in C - B, then x is in C and x is not in B. By the above note, this means that x is in C and x is not in A. Hence x is in C - A. (2) The converse is false. Let C = {1}, A = {1,2}, B = {1}. So, C - B = C - A are both empty sets (hence C - B is a subset of C - A), but A is not a subset of B. I hope that helps!