Archangel Macsika
Let A = {a,b,d,e,g,f,1,2,3}, B = {1,2,3}, and C = {1,2,3,a,d,g}. Find the following: (i) A ՈB Ս C (ii) A-B (iii) (B Ո C) x (A Ո C) (iv) P(B Ո C) (v) |CxA|
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Solution:
A = {a,b,d,e,g,f,1,2,3}, B = {1,2,3}, and C = {1,2,3,a,d,g}.
(i) A ՈB Ս C = (A ՈB) Ս C = {1,2,3} Ս {1,2,3,a,d,g} = {1,2,3,a,d,g}
(ii) A-B = {a,b,d,e,g,f}
(iii) (B Ո C) x (A Ո C) = {1,2,3} x {1,2,3,a,d,g} = {(1,1),(1,2),(1,3),(1,a),(1,d),(1,g),(2,1),(2,2),(2,3),(2,a),(2,d),(2,g),(3,1),(3,2),(3,3),(3,a),(3,d),(3,g)}
(iv) (B Ո C) = {1,2,3}
P(B Ո C) = {,{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}}
(v) |CxA| = |C|x|A| = 6x9 = 54