Question

QUESTION 1 The number of elements in sets A and B are shown in Figure 1.0. If n(A) = n(B) find: (a) x (b) n(A) (c) n(B) (d) n(AUB) 2x 4xx+5 Figure 1.0 10 marks​

Answer 1

From the given figure, we can write the following equations:

n(A) = 2x + 4

n(B) = x + 5

n(A∪B) = n(A) + n(B) - n(A∩B)

Since we are given that n(A) = n(B), we can substitute the expressions for n(A) and n(B) to get:

2x + 4 = x + 5

x = 1

(a) x = 1

(b) n(A) = 2x + 4 = 2(1) + 4 = 6

(c) n(B) = x + 5 = 1 + 5 = 6

(d) n(A∪B) = n(A) + n(B) - n(A∩B)

We still need to find n(A∩B) to calculate n(A∪B). Looking at the figure, we can see that there are 2 elements that are common to both A and B. Therefore,

n(A∩B) = 2

Substituting this value, we get:

n(A∪B) = n(A) + n(B) - n(A∩B) = 6 + 6 - 2 = 10

Therefore, (d) n(A∪B) = 10.

Explanation: