Mathematics
Let A = {b, d, e, f}, B = {c, d, g, h} and C = {e, f, g, h}. Find :
(i) A - B
(ii) B - C
(iii) C - A
(iv) (A - B) ∪ (B - A)
(v) (B - C) ∪ (C - B)
Sets
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Answer
(i) A - B
Given:
A = {b, d, e, f}
B = {c, d, g, h}
A - B = Elements of A which are not in B
A - B = {b, d, e, f} - {c, d, g, h} = {b, e, f}
∴ A - B = {b, e, f}
(ii) B - C
Given:
B = {c, d, g, h}
C = {e, f, g, h}
B - C = Elements of B which are not in C.
B - C = {c, d, g, h} - {e, f, g, h} = {c, d}
∴ B - C = {c, d}
(iii) C - A
Given:
C = {e, f, g, h}
A = {b, d, e, f}
C - A = Elements of C which are not in A.
C - A = {e, f, g, h} - {b, d, e, f} = {g, h}
∴ C - A = {g, h}
(iv) (A - B) ∪ (B - A)
Given:
A = {b, d, e, f}
B = {c, d, g, h}
(A - B) = {b, d, e, f} - {c, d, g, h} = {b, e, f}
(B - A) = {c, d, g, h} - {b, d, e, f} = {c, g, h}
(A - B) ∪ (B - A) = {b, e, f} ∪ {c, g, h} = {b, c, e, f, g, h}
∴ (A - B) ∪ (B - A) = {b, c, e, f, g, h}
(v) (B - C) ∪ (C - B)
Given:
B = {c, d, g, h}
C = {e, f, g, h}
B - C = {c, d, g, h} - {e, f, g, h} = {c, d}
(C - B) = {e, f, g, h} - {c, d, g, h} = {e, f}
(B - C) ∪ (C - B) = {c, d} ∪ {e, f} = {c, d, e, f}
∴ (B - C) ∪ (C - B) = {c, d, e, f}
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Related Questions
Let A = {a, b, c}, B = {b, d, e} and C = {e, f, g}, verify that :
(i) A ∪ B = B ∪ A
(ii) (A ∪ B) ∪ C = A ∪ (B ∪ C)
(iii) A ∩ B = B ∩ A
(iv) (A ∩ B) ∩ C = A ∩ (B ∩ C)
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(i) Write each one of the sets A, B, C in Roster form.
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(a) A ∪ B
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(ii) B'
(iii) A' ∩ B'
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(v) (A ∪ B)' = (A' ∩ B')
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(ii) (A ∩ B)' = (A' ∪ B')