Find the intersection of each pair of sets

Tuesday, 8 April 2014
Find the intersection of each pair of sets:
(i) X = {1, 3, 5} Y = {1, 2, 3}
(ii) A = {a, e, i, o, u} B = {a, b, c}
(iii) A = {x: x is a natural number and multiple of 3} B = {x: x is a natural number less than 6}
(iv) A = {x: x is a natural number and 1 < x ≤ 6} B = {x: x is a natural number and 6 < x < 10}

(v) A = {1, 2, 3}, B = Φ
Answer
In intersection we write common element of both sets.
(i) X = {1, 3, 5}, Y = {1, 2, 3} so X ∩ Y = {1, 3}
(ii) A = {a, e, i, o, u}, B = {a, b, c} so A ∩ B = {a}
(iii) Natural number and multiple of 3 are 3, 6, 9 …
Natural number less than 6 are {1, 2, 3, 4, 5, 6}
So that A ∩ B = {3}
(iv) ) Natural numbers greater than 1 and lower than and equal to 6 are 2, 3, 4, 5 and 6.
Natural number greater than 6 and less than 10 are 7, 8 and 9.
there are no common element in both sets.
So that A ∩ B ={} or Φ
(v) A = {1, 2, 3}, B = Φ here B is empty or null set so there is no common element. Hence, A ∩ B = Φ

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