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Edexcel IGCSE Math A Higher 1.5 Set Language and Notation Questions

Use set-notation questions to list members, complete Venn diagrams and calculate counts from unions, intersections and complements.

Syllabus
First assessment 2018
Course
Math A 4MA1
Level
Higher

Exam points

  • List members from unions, intersections, complements and empty-set statements.
  • Complete two- or three-set Venn diagrams from totals and region information.
  • Use Venn regions to find n(A), n(A ∩ B) or counts outside named sets correctly.

Covered syllabus points

1.5.A The definition of a set1.5.B Set notation1.5.C Universal and empty sets1.5.D Complements of sets1.5.E Venn diagrams to represent sets1.5.HA Algebraic sets and subsets1.5.HB Venn diagrams and numbers of elements1.5.HC The notation n(A) for the number of elements in the set1.5.HD Sets in practical situations

Question 1

[Maximum number: 5]

7E={23,24,25,26,27,28,29,30,31,32,33,34}7 \mathscr{E}=\{23,24,25,26,27,28,29,30,31,32,33,34\}A={A=\{ even numbers }\}B={23,29,31}B=\{23,29,31\}C={C=\{ multiples of 3}\}

Question (a)

(a)

List the members of the set

[ 2 ]

Question (i)

(i)

B∪CB \cup C

[ 1 ]

Question (ii)

(ii)

A′∩CA^{\prime} \cap C

[ 1 ]

Question (b)

(b)

Is it true that B∩C=∅B \cap C=\varnothing ?

Tick ( ✓ ) one of the boxes below.

Figure for Question (b) — Edexcel IGCSE Math A Higher

Give a reason for your answer.

The set D has 4 members and is such that D∩(A∪C)=∅D \cap(A \cup C)=\varnothing

[ 1 ]

Question (c)

(c)

List the members of set D

[ 2 ]

Question 2

[Maximum number: 3]

14E={14 \mathscr{E}=\{ positive integers less than 20}\}A={x:x<12}A=\{x: x<12\}B={x:7⩽x<16}B=\{x: 7 \leqslant x<16\}

Question (a)

(a)

List the members of A∩BA \cap B
C is a set such that C⊂AC \subset A and n(C)=3
Given that all members of C are even numbers,

[ 2 ]

Question (b)

(b)

list the members of one possible set C.

[ 1 ]

Question 3

[Maximum number: 6]

100 farmers are asked if they have goats (G), sheep (S) or chickens (C) on their farms.
Of these farmers
31 have sheep
53 have chickens
6 have goats, sheep and chickens
11 have sheep and goats
17 have sheep and chickens
18 have goats and chickens
20 do not have any goats, sheep or chickens

Question (a)

(a)

Using this information, complete the Venn diagram to show the number of farmers in each appropriate subset.

Figure for Question (a) — Edexcel IGCSE Math A Higher
[ 3 ]

Question (b)

(b)

Find

[ 3 ]

Question (i)

(i)

n(G)

[ 1 ]

Question (ii)

(ii)

n([G∪S]′)\mathrm{n}\left([G \cup S]^{\prime}\right)

[ 1 ]

Question (iii)

(iii)

n(G′∩C)\mathrm{n}\left(G^{\prime} \cap C\right)

One of the farmers who has chickens is chosen at random.

[ 1 ]

Question 4

[Maximum number: 2]

7E={23,24,25,26,27,28,29,30,31,32,33,34}7 \mathscr{E}=\{23,24,25,26,27,28,29,30,31,32,33,34\}A={A=\{ even numbers }\}B={23,29,31}B=\{23,29,31\}C={C=\{ multiples of 3}\}

List the members of set D

Question 5

[Maximum number: 2]

14E={14 \mathscr{E}=\{ positive integers less than 20}\}A={x:x<12}A=\{x: x<12\}B={x:7⩽x<16}B=\{x: 7 \leqslant x<16\}

List the members of A∩BA \cap B
C is a set such that C⊂AC \subset A and n(C)=3
Given that all members of C are even numbers,

Question 6

[Maximum number: 1]

7E={23,24,25,26,27,28,29,30,31,32,33,34}7 \mathscr{E}=\{23,24,25,26,27,28,29,30,31,32,33,34\}A={A=\{ even numbers }\}B={23,29,31}B=\{23,29,31\}C={C=\{ multiples of 3}\}

Is it true that B∩C=∅B \cap C=\varnothing ?

Tick ( ✓ ) one of the boxes below.

Figure for Question 6 — Edexcel IGCSE Math A Higher

Give a reason for your answer.

The set D has 4 members and is such that D∩(A∪C)=∅D \cap(A \cup C)=\varnothing

Question 7

[Maximum number: 1]

100 farmers are asked if they have goats (G), sheep (S) or chickens (C) on their farms.
Of these farmers
31 have sheep
53 have chickens
6 have goats, sheep and chickens
11 have sheep and goats
17 have sheep and chickens
18 have goats and chickens
20 do not have any goats, sheep or chickens

Find

n([G∪S]′)\mathrm{n}\left([G \cup S]^{\prime}\right)

Question 8

[Maximum number: 1]

Here is a Venn diagram.

Figure for Question 8 — Edexcel IGCSE Math A Higher

List the members of the set

A

Question 9

[Maximum number: 1]

14E={14 \mathscr{E}=\{ positive integers less than 20}\}A={x:x<12}A=\{x: x<12\}B={x:7⩽x<16}B=\{x: 7 \leqslant x<16\}

list the members of one possible set C.

Question 10

[Maximum number: 1]

100 farmers are asked if they have goats (G), sheep (S) or chickens (C) on their farms.
Of these farmers
31 have sheep
53 have chickens
6 have goats, sheep and chickens
11 have sheep and goats
17 have sheep and chickens
18 have goats and chickens
20 do not have any goats, sheep or chickens

Find

n(G)

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