Sets

3 marks · Hard

Let the universal set . Let , .

(a)

List the elements of P and Q.

[1 mark]

(b)

Find .

[1 mark]

(c)

How many elements are in ?

[1 mark]

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

Show answer

(a) P = {2, 4, 6, 8}; Q = {3, 6, 9}

(b) {3, 9}

Common mistakes: Forgetting to include endpoints; Confusing complements

Show mark scheme and worked solution

Marking points

B1 (a) · 1 mark · Lists correct elements of P and Q.

B2 (b) · 1 mark · Identifies P', lists P' ∩ Q correctly. (follow-through)

B3 (c) · 1 mark · Calculates correct number of elements in (P ∪ Q)' (follow-through)

Worked solution

a) P = {2, 4, 6, 8} (even numbers between 2 and 9). Q = {3, 6, 9} (multiples of 3 in U).

b) P' = U minus P = {1, 3, 5, 7, 9, 10}; Q = {3, 6, 9}; so P' ∩ Q = {3, 9}

c) P ∪ Q = {2, 3, 4, 6, 8, 9}, so (P ∪ Q)' = {1, 5, 7, 10}; this has 4 elements.