1. (10pts] Let A = {1, 2, 3, 4, 5}, let B = {1,4,5,7,8,9}, and let C = {2, 4, 6, 7,9}. Determine each of the following (a) An Bnc. (b) (AUB) N (AUC). (c) A - (BUC). (d) (A – C) (C – A)

Answer and explanation:Given : Let A = {1, 2, 3, 4, 5}, let B = {1,4,5,7,8,9}, and let C = {2, 4, 6, 7,9}.To find : Determine each of the following,a) [tex](A\cap B)\cap C[/tex]b) [tex](A\cup B)\cap (A\cup C)[/tex]c) [tex]A - (B\cup C)[/tex]d) [tex](A-C) (C-A)[/tex] Solution : The union of two sets is a new set that contains all of the elements that are in at least one of the two sets. The intersection of two sets is a new set that contains all of the elements that are in both sets.a) [tex](A\cap B)\cap C[/tex][tex]A\cap B=\{1,4,5\}[/tex]Then, [tex](A\cap B)\cap C=\{4\}[/tex]b) [tex](A\cup B)\cap (A\cup C)[/tex][tex]A\cup B=\{1,2,3,4,5,7,8,9\}[/tex][tex]A\cup C=\{1,2,3,4,5,7,9\}[/tex][tex](A\cup B)\cap (A\cup C)=\{1,2,3,4,5,7,9\}[/tex]c) [tex]A - (B\cup C)[/tex][tex]B\cup C=\{1,2,4,5,6,7,8,9\}[/tex][tex]A - (B\cup C)=\{3\}[/tex]d) [tex](A-C) (C-A)[/tex][tex]A-C=\{1,3,5\}[/tex][tex]C-A=\{6,7,9\}[/tex][tex](A-C) (C-A)=\{1,3,5\}\times\{6,7,9\}[/tex][tex](A-C) (C-A)=\{(1,6),(1,7),(1,9),(3,6),(3,7),(3,9),(5,6),(5,7),(5,9)\}[/tex]