Sets

4 marks · Normal

The Venn diagram below represents sets and in the universal set .

Venn diagram showing sets X and Y within U. Each region labelled with numbers.

(a)

List the elements of set .

[1 mark]

(b)

List the elements of set .

[1 mark]

(c)

Write down the elements of .

[1 mark]

(d)

List the elements in that are not in or .

[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.

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(a) {2, 3}

(b) {3, 5}

(d) {8}

Also accept: Order of elements need not match diagram; labels used as set elements.

Common mistakes: Omitting elements in both sets from intersection; misidentifying regions outside both circles.

Show mark scheme and worked solution

Marking points

C1 (a) · 1 mark · Correct list of elements in set X: {2, 3}

C2 (b) · 1 mark · Correct list of elements in set Y: {3, 5}

C3 (c) · 1 mark · Correct intersection: {3}

C4 (d) · 1 mark · Correct complement: {8}

Worked solution

a) X contains 2 (only in X) and 3 (in both). So, X = {2, 3}.

b) Y contains 3 (in both) and 5 (only in Y). So, Y = {3, 5}.

c) X ∩ Y is the region in both; only 3, so {3}.

d) The outside region is element 8, so answer is {8}.