Mathematics
Let A = {x : x is a multiple of 2, x < 15}, B = {x : x is a multiple of 3, x < 20}, C = {x : x is a prime, x < 20}.
(i) Write each one of the sets A, B, C in Roster form.
(ii) Find:
(a) A ∪ B
(b) A ∪ C
(c) B ∪ C
(d) A ∩ B
(e) A ∩ C
(f) B ∩ C
Sets
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Answer
(i) Write each one of the sets A, B, C in Roster form.
Given:
A = {x : x is a multiple of 2, x < 15}
Multiples of 2 less than 15 are: 2, 4, 6, 8, 10, 12, 14.
A = {2, 4, 6, 8, 10, 12, 14}
B = {x : x is a multiple of 3, x < 20}
Multiples of 3 less than 20 are: 3, 6, 9, 12, 15, 18.
B = {3, 6, 9, 12, 15, 18}
C = {x : x is a prime, x < 20}
Prime numbers between 1 and 20 are: 2, 3, 5, 7, 11, 13, 17, 19.
C = {2, 3, 5, 7, 11, 13, 17, 19}
∴ A = {2, 4, 6, 8, 10, 12, 14}, B = {3, 6, 9, 12, 15, 18} and C = {2, 3, 5, 7, 11, 13, 17, 19}
(ii) Find:
(a) A ∪ B
Given:
A = {2, 4, 6, 8, 10, 12, 14}
B = {3, 6, 9, 12, 15, 18}
A ∪ B = {2, 4, 6, 8, 10, 12, 14} ∪ {3, 6, 9, 12, 15, 18} = {2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 18}
∴ A ∪ B = {2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 18}
(b) A ∪ C
Given:
A = {2, 4, 6, 8, 10, 12, 14}
C = {2, 3, 5, 7, 11, 13, 17, 19}
A ∪ C = {2, 4, 6, 8, 10, 12, 14} ∪ {2, 3, 5, 7, 11, 13, 17, 19} = {2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 17, 19}
∴ A ∪ C = {2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 17, 19}
(c) B ∪ C
Given:
B = {3, 6, 9, 12, 15, 18}
C = {2, 3, 5, 7, 11, 13, 17, 19}
B ∪ C = {3, 6, 9, 12, 15, 18} ∪ {2, 3, 5, 7, 11, 13, 17, 19} = {2, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17, 18, 19}
∴ B ∪ C = {2, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17, 18, 19}
(d) A ∩ B
Given:
A = {2, 4, 6, 8, 10, 12, 14}
B = {3, 6, 9, 12, 15, 18}
A ∩ B = {2, 4, 6, 8, 10, 12, 14} ∩ {3, 6, 9, 12, 15, 18} = {6, 12}
∴ A ∩ B = {6, 12}
(e) A ∩ C
Given:
A = {2, 4, 6, 8, 10, 12, 14}
C = {2, 3, 5, 7, 11, 13, 17, 19}
A ∩ C = {2, 4, 6, 8, 10, 12, 14} ∩ {2, 3, 5, 7, 11, 13, 17, 19} = {2}
∴ A ∩ C = {2}
(f) B ∩ C
Given:
B = {3, 6, 9, 12, 15, 18}
C = {2, 3, 5, 7, 11, 13, 17, 19}
B ∩ C = {3, 6, 9, 12, 15, 18} ∩ {2, 3, 5, 7, 11, 13, 17, 19} = {3}
∴ B ∩ C = {3}
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