Question

- If A = {3, 4,5} and B = {5, 6, 7, 8} then find (1) AU B.(II) A B. (1) A - B and (iv) B - A and
also verify the following.
(a) A U B = B U A​

Answer 1

Step-by-step explanation:

Given:-

A = {3, 4,5} and B = {5, 6, 7, 8}

To find:-

If A = {3, 4,5} and B = {5, 6, 7, 8} then find (1) AU B.(II) A n B. (1) A - B and (iv) B - A and also verify the following.

(a) A U B = B U A

Solution:-

Given sets are :

A = {3, 4,5}

B = {5, 6, 7, 8}

1)AUB= {3, 4,5} U {5, 6, 7, 8} =

{3,4,5,6,7,8}-----(1)

2)AnB ={3, 4,5} n {5, 6, 7, 8} = {5}

3) A-B = {3, 4,5} - {5, 6, 7, 8} = { 3,4}

4)B-A={5,6,7,8} - {3,4,5} = {6,7,8}

5) BUA ={5,6,7,8} U {3,4,5} =

{3,4,5,6,7,8,} -----(2)

From (1)&(2)

AUB = BUA

Answer:-

• AUB={3,4,5,6,7,8}
• AnB={5}
• A-B={3,4}
• B-A={6,7,8}
• BUA={3,4,5,6,7,8}
• AUB=BUA
• Commutative property under union of the sets holds good.