Question

Let A = (x: x is a letter in the word CHANDIGARH) and
B = (x x is a letter in the word RAJASTHAN)
1. Find An B and AUB
II. Find n(a), n(b), n(AnB) and n(AUB)
II. Verify: n (AUB) = n (a) + n (b) - n (AnB)
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Answer 1

Answer:

A = (x: x is a letter in the word CHANDIGARH)

A = { A,C,D,G,H,I,N,R}

B = (x x is a letter in the word RAJASTHAN)

B = { A , H, J,N, R, S ,T }

1. Find An B and AUB

AnB = { A,C,D,G,H,I,N,R} n {A,H,J,N,R,S,T}

= { A,H,N,R}

AUB = {A,C,D,G,H,I,N,R}U{A,H,J,N,R,S,T }

= { A,C,D,G,H,I,J,N,R,S,T}

II. Find n(a), n(b), n(AnB) and n(AUB)

n(A) = 8,

n(B) = 7,

n(AnB) = 4,

n(AUB) = 11

II. Verify: n (AUB) = n (a) + n (b) - n (AnB)

RHS = n(A) + n(B) - n(AnB)

= 8 + 7 - 4

= 15 - 4

= 11

= n(AUB)

= LHS

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