Question

If u={4,7,8,10,11,12,15,16},a={7,8,11,12}, and b={4,8,12,15},then verify de morgan's laws for complementation

Answer 1

Answer:

De Morgans laws

(A∪B)´⁼A´∩B´

(A∩B)´⁼A´∪B´

Step-by-step explanation:

U=(4,7,8,10,11,12,15,17)

A=(7,8,11,12)

B=(4,8,12,15)

A∪B=(4,7,8,11,12,15)

(A∪B)′=(10,16)············(1)

A′=(4,10,15,16)

B′=(7,10,11,16)

(A′∩B′)=(10,16)··········⁽2)

From (1) and (2) are equal.

Hence (A∪B)′=A′∩B′

A∩B=(8,12)

(A∩B)′=(4,7,10,11,15,16)·······⁽3)

(A′∪B′)=(4,7,10,11,15,16)·······⁽4)

From (3) and (4) are equal

Hence (A∩B)′=A′∪B′