iGCSE Mathematics (0580) :E1.2 Use language, notation and Venn diagrams to describe sets and represent relationships between sets. iGCSE Style Questions Paper 2

Question

The Venn diagram shows the elements of the sets E, P and Q.
Complete the statements.

(a) P = {……}

(b) n(P ∪ Q) = ……

▶️ Answer/Explanation

Solution

Ans:

(a) P = {a, b, c, d}

(b) n(P ∪ Q) = 6

For (a), list all elements in circle P.

For (b), count all unique elements in P and Q combined.

Question

(a) On the Venn diagram, shade the region P ∪ Q′.

(b) n(ξ) = 20, n(A ∪ B)′ = 1, n(A) = 12, n(B) = 10

Complete the Venn diagram.

▶️ Answer/Explanation

Solution

(a) Ans:

P ∪ Q′ means all elements in P or not in Q.

(b) Ans:

n(A ∩ B) = n(A) + n(B) – n(A ∪ B) = 12 + 10 – 19 = 3

A only = 12 – 3 = 9, B only = 10 – 3 = 7, outside = 1

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