Question

1. For A = {1,3,5,7,9}, B = {2, 3, 4, 6, 7, 8} and the universal set U = {1, 2, ..., 10}, determine the following: (a) An B. (b) AUB. (c) A – B. (d) B – A. (e) A e B. (f) Ā. (g) B.

Answer 1

(a) { 3,7 }

(b) { 1,2,3,4,5,6,7,8,9}

(c) {1,5,9 }

(d) {2,4,6,8}

(e) { 3,7}

(f) { 2,4,6,8,10}

{g} {2,3,4,6,7,8}

Explanation:

We have given A={1,3,5,7,9}, B={2,3,4,6,7,8}

Universal set U={1,2,3,4,5,6,7,8,9,10}

We have to find

(a)
`A\cap B` = {1,3,5,7,9}
`\cap` {2,3,4,6,7,8} ={ 3,7 }

(B)
`A\cup B[/tex = {1,3,5,7,9}[tex]\cup` {2,3,4,6,7,8} ={ 1,2,3,4,5,6,7,8,9}

(c) A-B = {1,3,5,7,9}- {2,3,4,6,7,8} = {1,5,9 }

(d) B-A = {2,3,4,6,7,8} - {1,3,5,7,9} = {2,4,6,8}

(E)
`A\in\ B` = {1,3,5,7,9}
`\in` { 2,3,4,6,7,8} = { 3,7}

(f)
`\bar{A}=U-A` = {1,2,3,4,5,6,7,8,9,10} - {1,3,5,7,9} = { 2,4,6,8,10}

(g) B = {2,3,4,6,7,8}