Question

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 1

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) $(A\cap B)\cap C$

b) $(A\cup B)\cap (A\cup C)$

c) $A - (B\cup C)$

d) $(A-C) (C-A)$

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) $(A\cap B)\cap C$

$A\cap B=\{1,4,5\}$

Then, $(A\cap B)\cap C=\{4\}$

b) $(A\cup B)\cap (A\cup C)$

$A\cup B=\{1,2,3,4,5,7,8,9\}$

$A\cup C=\{1,2,3,4,5,7,9\}$

$(A\cup B)\cap (A\cup C)=\{1,2,3,4,5,7,9\}$

c) $A - (B\cup C)$

$B\cup C=\{1,2,4,5,6,7,8,9\}$

$A - (B\cup C)=\{3\}$

d) $(A-C) (C-A)$

$A-C=\{1,3,5\}$

$C-A=\{6,7,9\}$

$(A-C) (C-A)=\{1,3,5\}\times\{6,7,9\}$

$(A-C) (C-A)=\{(1,6),(1,7),(1,9),(3,6),(3,7),(3,9),(5,6),(5,7),(5,9)\}$