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SETS WORKSHEET
1) List the following sets:
A = {odd numbers less than 16}
B = {capitals of countries in the United Kingdom}
C = {numbers which divide exactly into 24}
2) Write the following sets using a description instead of a list:
X = {1, 4, 9, 16, 25, 36, 49, 64, 81}
Y = {John Lennon, Paul McCartney, George Harrison, Ringo Starr}
Z = {12, 14, 16, 18}
3)(a) For the sets in questions 1, what is n(A), n(B), n(C)?
(b) Is n(A) = n(C) ?
(c) Is A = C ?
4) In this question we are using the following sets:
P={multiples of 3} Q={integers less than 12} R={prime numbers}
Copy and complete the following using either  or  :
(a) 7 ... Q (b) 7 ... P (c) 7 ... R (d) 13 ... Q (e) 13 ... R (f) 99 ... P
5) Which of the following are equal to ∅ ?
(a) {members of your class over 2 metres tall}
(b) {triangles with 4 sides}
(c) {men who have stood on the moon}
6) Copy each of the following and write after it true (T) or false (F)
(a) {2, 3, 4} ⊂ {1, 2, 3, 4, 5} (b) {1, 2, 3, 4, 5} ⊂ {2, 3, 4}
(c) {3, 5, 6} ⊂ {multiples of 3} (d) {2, 4, 6} ⊂ {2, 4, 6}
(e) ∅ ⊂ {2, 4, 6} (f) If A ⊂ B then n(A) ≤ n(B)
(g) n(∅) = 0 (h) If n(A) ≤ n(B) then A ⊂ B
7) (a) List all the subsets of {a, b, c}
(b) List all the subsets of {a, b}
(c) List all the subsets of {a}
(d) List all the subsets of ∅
(e) Use your answers to parts (a) to (d) to copy and complete this
table, and then write down a rule about what you notice from the
table.
Set A n(A) No of subsets of A
∅ 0
{a} 1
{a,b} 2
{a,b,c} 3
(f) According to your rule, how many subsets should there be of
{a,b,c,d}? Check your rule by writing them all down.
8) In this question we are using the following sets:
A = {1, 2, 3, 4, 5} B = {1, 3, 5}
C = {even numbers less than 20} D = {prime numbers less than 20}
List the following sets:
(a) C (b) D (c) A  C (d) A  D (e) A  B (f) B  C
(g) C  D (h) What set is A  B the same as? Why is this?
9) Draw Venn Diagrams to illustrate the following sets:
(a) E = {1,2,3,....12}, A = {odd numbers}, B = {factors of 12}
(b) E = {1,2,3,....12}, P = {3,5,7}, Q = {prime numbers}
(c) E = {1,2,3,....12}, X = {odd numbers}, Y = {multiples of 4}
(d) E = {a,b,c,...j}, A = {vowels}, B = {letters in the word "cabbage"}
(e) E = {1,2,3,...12}, P = {even numbers}, Q = {multiples of 4}

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WS1-Sets.pdf

  • 1. SETS WORKSHEET 1) List the following sets: A = {odd numbers less than 16} B = {capitals of countries in the United Kingdom} C = {numbers which divide exactly into 24} 2) Write the following sets using a description instead of a list: X = {1, 4, 9, 16, 25, 36, 49, 64, 81} Y = {John Lennon, Paul McCartney, George Harrison, Ringo Starr} Z = {12, 14, 16, 18} 3)(a) For the sets in questions 1, what is n(A), n(B), n(C)? (b) Is n(A) = n(C) ? (c) Is A = C ? 4) In this question we are using the following sets: P={multiples of 3} Q={integers less than 12} R={prime numbers} Copy and complete the following using either  or  : (a) 7 ... Q (b) 7 ... P (c) 7 ... R (d) 13 ... Q (e) 13 ... R (f) 99 ... P 5) Which of the following are equal to ∅ ? (a) {members of your class over 2 metres tall} (b) {triangles with 4 sides} (c) {men who have stood on the moon} 6) Copy each of the following and write after it true (T) or false (F) (a) {2, 3, 4} ⊂ {1, 2, 3, 4, 5} (b) {1, 2, 3, 4, 5} ⊂ {2, 3, 4} (c) {3, 5, 6} ⊂ {multiples of 3} (d) {2, 4, 6} ⊂ {2, 4, 6} (e) ∅ ⊂ {2, 4, 6} (f) If A ⊂ B then n(A) ≤ n(B) (g) n(∅) = 0 (h) If n(A) ≤ n(B) then A ⊂ B 7) (a) List all the subsets of {a, b, c} (b) List all the subsets of {a, b} (c) List all the subsets of {a} (d) List all the subsets of ∅ (e) Use your answers to parts (a) to (d) to copy and complete this table, and then write down a rule about what you notice from the table. Set A n(A) No of subsets of A ∅ 0 {a} 1 {a,b} 2 {a,b,c} 3 (f) According to your rule, how many subsets should there be of {a,b,c,d}? Check your rule by writing them all down. 8) In this question we are using the following sets: A = {1, 2, 3, 4, 5} B = {1, 3, 5} C = {even numbers less than 20} D = {prime numbers less than 20} List the following sets: (a) C (b) D (c) A  C (d) A  D (e) A  B (f) B  C (g) C  D (h) What set is A  B the same as? Why is this? 9) Draw Venn Diagrams to illustrate the following sets: (a) E = {1,2,3,....12}, A = {odd numbers}, B = {factors of 12} (b) E = {1,2,3,....12}, P = {3,5,7}, Q = {prime numbers} (c) E = {1,2,3,....12}, X = {odd numbers}, Y = {multiples of 4} (d) E = {a,b,c,...j}, A = {vowels}, B = {letters in the word "cabbage"} (e) E = {1,2,3,...12}, P = {even numbers}, Q = {multiples of 4}