Lct A 8 and S be ets a Prove that if AB sin SIB 6 prove that

Lct A, 8, and S be ets a) Prove that if AB, sin SIB 6) prove that A S iff A. S1(SIA)

Solution

A, B and S are the sets

Given that A is a subset of B

S \\ A = (S-A), the elements that belong to S but not belong to A

S \\ B = (S-B), the elements that belong to S but not belong to B

So we need to prove that S\\A is a subset of S\\B

Let us assume x belongs to S and x doesn\'t belong to B

Hence x belongs to S\\B and since A is a subset of B, hence S\\A also will be having the element X, therefore we can write the above equality as

S\\A is a subset of S\\B

b) A is a subset of S

S\\A will contain the element that belongs to the set S but not to A

S\\(S\\A) will contain the element that belong to the Set S but not A

Set S elements - (Set S elements - Set A elements) = Set S elements - Set S elements + Set A elements

= Set A elements

Hence the above thing is proved