1 Answer

Michael Malura · Answer 1 · 2020-08-09T12:19:12+0000

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)

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

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

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

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

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