Question

Let A and B be two sets such that: n (A) = 20, n (A U B ) = 42 and n ( A B ) = 4 Find (i) n (B ) (ii) n (A – B ) (iii) n ( B – A )

Answer 1

Given:
n(A)=20, 
n(A∪B)=42
 n(A∩B)=4

(i)
n(A∪B)=n(A)+n(B)−n(A∩B)
42=20+n(B)−4
n(B)=42−20+4=26

(ii
 n(A−B)=n(A)−n(A∩B)
n(A−B)=20−4=16

(iii
 n(B−A)=n(B)−n(A∩B)
n(B−A)=26−4=22

Answer 2

A set is a mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.

n(A∪B)$=n(A)+n(B)-n$(A∩B)

$n(B)=42-0+4=26$

$n(A-B)=n(A)-n$(A∩B)$=20-4=16$

$n(B-A)=n(B)-n$(A∩B)$=26-4=22$

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