Question

If U={4,8,12;16,20} then find U` and { }`.

Dont give copied answers!​

Answer 1

Answer:

MATHS

If U={4,8,12,16,20,24,28},A={8,16,24},B={4,16,20,28}.

Verify that (A∩B)′=A′∪B′

Step-by-step explanation:

The given sets are U={4,8,12,16,20,24,28}, A={8,16,24} and B={4,16,20,28}

We know that the complement of set A is  A′=U−A.

 

Consider the following:

(A∩B)′=U−(A∩B)={4,8,12,16,20,24,28}−[{8,16,24}∩{4,16,20,28}]

={4,8,12,16,20,24,28}−{16}={4,8,12,20,24,28}......(1)

A′∪B′=[U−A]∪[U−B]=[{4,8,12,16,20,24,28}−{8,16,24}]∪[{4,8,12,16,20,24,28}−{4,16,20,28}]

={4,12,20,28}∩{8,12,24}={4,8,12,20,24,28}......(2)

From equations 1 and 2, we get that (A∩B)′=A′∪B′.

Hence, (A∩B)′=A

Answer 2

Solution:

U={4,8,12,6,20}

U`=U-U:

U`=U-U={4,8,12,16,20}-{4,8,12,16,20}

= { } (ans)

{ }`=U-{ }:

{ }`=U-{ }={4,8,12,16,20} - { }

={4,8,12,16,20} (ans)