Question

IF A= {1,2,3,4} AND B={3,4,5,6} con AND c= {1, 2, 6,7}
VERIFY.
(AUB)INTERSECTION C=(A INTERSECTION C) U (B INTERSECTION C)​

Answer 1

Given :-

• If A= {1,2,3,4} AND B={3,4,5,6} and C = {1, 2, 6,7}

To find :-

• Verify
• (A U B) ∩ C = (A ∩ C) U (B ∩ C)

Solution :-

• A = {1,2,3,4}

• B = {3,4,5,6}

• C = {1, 2, 6,7}

→ (A U B) ∩ C = (A ∩ C) U (B ∩ C)

LHS = (A U B) ∩ C

• (A U B)

→ {1, 2, 3, 4, 5, 6}

• (A U B) = {1, 2, 3, 4, 5, 6}

Now,

→ (A U B) ∩ C = {1, 2, 6}

• LHS → (A U B) ∩ C = {1, 2, 6}

So,

RHS = (A ∩ C) U (B ∩ C)

• (A ∩ C) = {1, 2}

Now,

• (B ∩ C) = {6}

• RHS → (A ∩ C) U (B ∩ C) = {1, 2, 6}

Therefore,

• LHS = RHS verified

More to know :-

• Union of set

→ The union of A and B is a set of all those element which belongs either to A or to B or to both A and B

→ It is denoted by A U B (read as A union B)

• Intersection of set

→ The intersection of A and B is a set of all those elements that belongs to both A and B

→ It is denoted by A ∩ B (read as A intersection B)