Question

Let U = { x / x € N , x < 25 } is a universal set.
A = { a / a is a prime number < 25 a€ N }
B = { b / b is a odd number <25 , b € N }
Prove that
1. (AUB)' = A' intersection B'
2. (A intersection B)' = A' U B'

Answer 1

Step-by-step explanation:

U={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25}

A={2,3,5,7,11,13,17,19,23}

B={1,3,5,7,9,11,13,15,17,19,21,23,25}

AUB={1,2,3,5,7,9,11,13,15,17,19, 21, 23,25}

(AUB)'={4,6,8,10,12,14,16,18,20,22,24}

(A intersection B)={3,5,7,11,13,17,19,23}

(A intersection B)'={1,2,4,6,8,9,10,12,14,15,16,18, 20, 21, 22, 24, 25}

Hence,proved

(AUB)'={4,6,8,10,12,14,16,18,20,22,24}

(A intersection B)'={1,2,4,6,8,9,10,12,14,15,16,18, 20, 21, 22, 24, 25}