Question

Let U ={1, 2, 3; 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find (i) (ii) (iii) (iv) (v) (vi)

Answer 1

(i)

Given universal set is { 1,2,3,4,5,6,7,8,9 } .

A = { 1, 2, 3, 4 }

Therefore, A ′ =U−A={ 5,6,7,8,9 } .

(ii)

B={ 2,4,6,8 }

Therefore, B'={ 1,3,5,7,9 } .

(iii)

A∪C={ 1,2,3,4,5,6 }

Therefore, ( A∪C )'={ 7,8,9 }

(iv)

A∪B={ 1,2,3,4,6,8 }

Therefore, ( A∪B )'={ 5,7,9 }

(v)

A ′ ={ 5,6,7,8,9 }

Thus, ( A ′ ) ′ ={ 1,2,3,4 }=A

(vi)

B∩C={ 4,6 } B−C=B−(B∩C) ={ 2,4,6,8 }−{ 4,6 } ={ 2,8 }

Therefore, ( B−C )'={ 1,3,4,5,6,7,9 } .