Tuesday, May 10, 2022

A = {y:y=a+12,aWanda5}

a = {0, 1, 2, 3, 4, 5}

⇒ y = a+12=12

y = 1+12=22 = 1

y = 2+12=32

y = 3+12=42 = 2

y = 4+12=52

y = 5+12=62 = 3

∴ A = {12,1,32,2,52,3}

B = {y:y=2n12,nWandn<5}

n = {0, 1, 2, 3, 4}

⇒ y = 2×0-12=-12

y = 2×1-12=12

y = 2×2-12=32

y = 2×3-12=52

y = 2×4-12=72

∴ B = {-12,12,32,52,72}

C = {-1,-12,1,32,2}

B ∪ C = {-1,-12,12,1,32,2,52,72}

A − (B ∪ C) = {3}    ...(1)

A − B = {1, 2, 3}

A − C = {12,52,3}

(A – B) ∩ (A – C) = {3}  ...(2)

From (1) and (2), it is verified that

A – (B ∪ C) = (A – B) ∩ (A – C).

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