Answer to Question #230544 in Discrete Mathematics for Mak Kin Yun Riva

Question

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|

Answer 1

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) = {$\phi$,{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}}

(v) |CxA| = |C|x|A| = 6x9 = 54