Q2 of 162 Page 1

Let A = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7}. Verify the following identities:

A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

L.H.S.


(B ∪ C) = {x: x ϵ B or x ϵ C }


= {2, 3, 4, 5, 6, 7}.


(A ∩ (B ∪ C)) = {x:x ϵ A and x ϵ (B ∪ C)}


= {2, 4, 5}


R.H.S:


(A ∩ B) = {x:x ϵ A and x ϵ B}


= {2, 5}


(A ∩ C) = {x:x ϵ A and x ϵ C}


= {4, 5}


(A ∩ B) ∪ (A ∩ C) = {x:x ϵ (A∩B) and x ϵ (A∩C) }.


= {2, 4, 5}.


Hence verified.


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1

Find the smallest set A such that A ∪ {1, 2} = {1, 2, 3, 5, 9}.

 2

Let A = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7}. Verify the following identities:

A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)

 2

Let A = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7}. Verify the following identities:

A ∩ (B – C) = (A ∩ B) – (A ∩ C)

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A– (B ∪ C) = (A – B) ∩ (A–C)