Question

a
SEC-B
Alaswer the following 4xs-20)
)
o It A={1,5. 6. 7 ay
€115.6.7ay and B-
and B-{3,4,5,69 and c={1,2,3,48 Prova
that AUBnC) = (AUB)N (AUC)​

Answer 1

Answer:

AU(B∩C) = (AUB) ∩ (AUC)​

Step-by-step explanation:

A={1,5, 6, 7} B={3,4,5,6,9} and C={1,2,3,4,8 )

B∩C ={3,4}

So LHS= AU(B∩C)={3,4} U {1,5, 6, 7}

AU(B∩C)={ 1,3,4,5,6,7}.........................(1)

*********************

For RHS AUB ={1,3,4,5,6,7,9}

AUC={1,5. 6. 7}U {1,2,3,4,8}

={1,2,3,4,5,6,7,8}

Thus RHS = (AUB) ∩ (AUC)​

{1,3,4,5,6,7,9} ∩ {1,2,3,4,5,6,7,8}

(AUB) ∩ (AUC)​ = { 1,3,4,5,6,7}..................(2)

From(1) and (2)

AU(B∩C) = (AUB) ∩ (AUC)​