Question

f A = {1, 2, 3, 4}, B = {3, 4, 5, 6},

C = {4, 5, 6, 7, 8} and universal set

X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify

the following:

i) A∪(B∩C) = (A∪B) ∩(A∪C)

​

Answer 1

Answer:

1 ans).AU(B(intersection)C)

{1,2,3,4}U{4,5,6}.

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

2. (AUB) Intersection (AUC)

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

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

1. LHS=2.RHS

HENCE PROVED

Step-by-step explanation:

In union we take each element of all sets except repetition but in intersection we take which in common in both sets

make it brainlist

Answer 2

Step-by-step explanation:

AU(B∩C)=(AUB)∩(AUC)

L.H.S.

AU(B∩C)

B∩C ={3,4,5,6}∩{4,5,6,7,8}

B∩C={4,5,6}

AU(B∩C)={1,2,3,4}U{4,5,6}

AU(B∩C)={1,2,3,4,5,6}

R.H.S.

(AUB)∩(AUC)

(AUB)={1,2,3,4}U{3,4,5,6}

(AUB)={1,2,3,4,5,6}

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

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

(AUB)∩(AUC)={1,2,3,4,5,6}∩{1,2,3,4,5,6,7,8}

(AUB)∩(AUC)={1,2,3,4,5,6}

L.H.S=R.H.S

AU(B∩C)=(AUB)∩(AUC)

SO,PROVED IT VERY EASYILY

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