If U={1,2,3,4,5,6,7,8,9},A={2,4,6,8} and B={2,3,5,7}. Verify that (i) (A∪B)′=A′∩B′(ii)(A∩B)′=A′∪B′
(i) Compute that (A∪B)'=A'∩B'
We are given, U={1,2,3,4,5,6,7,8,9},A={2,4,6,8} and B={2,3,5,7}
⇒A∪B=2,3,4,5,6,7,8⇒(A∪B)'=U-A∪B=1,9
Also
A'=U-A={1,3,5,7,9}B'=U-B={1,4,6,8,9}
On solving,
A'∩B'={1,9}
Therefore,(A∪B)′=A′∩B′, proved.
(ii) Compute that (A∩B)′=A′∪B′
We have,
A∩B=2
That is
(A∩B)'=U-(A∩B)={1,2,3,4,5,6,7,8,9}-2={1,3,4,5,6,7,8,9}
A'∪B'={1,3,5,7,9}∪{1,4,6,8,9}A'∪B'={1,3,4,5,6,7,8,9}
So we get,(A∩B)′=A′∪B′.
Hence, proved.
(I)(A∪B)′=A′∩B′
(ii)(A∩B)′=A′∪B′.
Let U = {1,2,3,4,5,6,7,8,9},
A = {2,4,6,8} and B = {2,3,5,7}.
Verify that :
(i) (A∪B)′=A′∩B′
(ii) (A∩B)′=A′∪B′.
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) A′ (ii) B′ (iii) (A∩C)′
(iv) (A∪B)′ (v) (A′)′ (vi) (B−C)′