Prove the second associative law from Table 1 by showing that if A,b. and C are sets, then A ∩ (b ∩ C) = (A ∩ B) ∩ C

Step 1:

Consider the three sets A and b and C we have to prove that

Which is associative law of sets for union

Step 2:

Definition:

(1)Let A and B are two sets then then two sets A and B are said to be equal if these two sets are subset of each other that is A=B if and

(2)

Step 3:

Here we prove that L.H.S(left hand side) is subset of R.H.S(left hand side) and R.H.S(left hand side) is subset of L.H.S(left hand side)

Consider L.H.S,

Let then by definition

Then again by definition,

Thus if then

…(1)