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

Answer

(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}

Step-by-step 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}