Question

33) Find A∪B, A∩B, A–B and B–A for the following sets. Given A = {2, 6, 10, 14} and B = {2, 5, 14, 16}​

Answer 1

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}