1.

Find A ∪ B, A ∩ B, A – B and B – A for the following sets.(i) A = {2, 6, 10, 14} and B = {2, 5, 14, 16}(ii) A = {a, b, c, e, u} and B = {a, e, i, o, u}(iii) A = {x : x ∈ N, x ≤ 10} and B = {x : x ∈ W, x < 6}(iv) A = Set of all letters in the word “mathematics” and B = Set of all letters in the word “geometry”

Answer»

(i) A = {2, 6, 10, 14} and B = {2, 5, 14, 16}

A ∪ B = {2, 6, 10, 14} ∪ {2, 5, 14, 16} = {2, 5, 6, 10, 14, 16}

A ∩ B = {2, 6, 10, 14} ∩ {2, 5, 14, 16} = {2, 14}

A – B = {2, 6, 10, 14} – {2, 5, 14, 16} = {6, 10}

B – A = {2, 5, 14, 16} – {2, 6, 10, 14} = {5, 16}

(ii) A = {a, b, c, e, u} and B = {a, e, i, o, u}

A ∪ B = {a, b, c, e, u} ∪ {a, e, i, o, u} = {a, b, c, e, i, o, u}

A ∩ B = {a, b, c, e, u} ∩ {a, e, i, o, u} {a, e, u}

A – B = {a, b, c, e, u} – {a, e, i, o, u} = {b, c}

B – A = {a, e, i, o, u} – {a, b, c, e, u} = {i, o}

(iii) x ∈ {1, 2, 3, ...}; x ∈ {0, 1, 2, 3, 4, 5, ...}

A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

B = {0, 1, 2, 3, 4, 5}

A ∪ B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} ∪ {0, 1, 2, 3, 4, 5}

= {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A ∩ B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} ∩ {0, 1, 2, 3, 4, 5}

= {1, 2, 3, 4, 5}

A – B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} – {0, 1, 2, 3, 4, 5}

= {6, 7, 8, 9, 10}

B – A = {0, 1, 2, 3, 4, 5} – {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

= {0}

(iv) A= {m, a, t, h, e, i, c, s}, B = {g, e, o, m, t, r, y}

A ∪ B = {m ,a, t, h, e, i, c, s} ∪ {g, e, o, m, t, r, y} = {m, a, t, h, e, i, c, s, g, o, r, y)

A ∩ B = {m, a, t, h, e, i, c, s} ∩ {g, e, o, m, t,r,y} = {m, t, e}

A – B = {m ,a, t, h, e, i, c, s} ∪ {g, e, o, m, t, r, y} = {a, h, i, c, s}

B – A = {m, a, t, h, e, i, c, 5} ∩ {g, e, o, m, t,r,y} = {g,o, r, y}


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