iGCSE Mathematics (0580) : C1.2 Understand notation of Venn diagrams.Definition of sets iGCSE Style Questions Paper 1

Question

There are 50 families in a village.

C = {families who own a car}
B = {families who own a bicycle}

23 families own a car.
10 families own a car and a bicycle.
6 families own no cars and no bicycles.

(a) Complete the Venn diagram.

(b) Find n(C∪B).

▶️ Answer/Explanation

Solution

Ans: (a) Venn diagram: Only car = 13, Both = 10, Only bicycle = 21, Neither = 6

(b) 44

(a) Only car = 23 – 10 = 13. Total accounted for = 13 + 10 + 6 = 29, so only bicycle = 50 – 29 = 21.

(b) n(C∪B) = Total – neither = 50 – 6 = 44, or 13 + 10 + 21 = 44.

Question

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

(a) Write down the elements of set P.

(b) Find n(P ∪ Q).

▶️ Answer/Explanation

Solution

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

These are the elements shown inside circle P.

(b) 6

Counting all elements in P or Q gives 6 elements.

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