Answer
(a)
First, perform the operation inside the parentheses of the set\[A\cap \left( B\cup C \right)\].
Now, compute\[B\cup C\].
Set \[B\cup C\] contains all the elements thatare in setB,setC,or both.
In the provided Venn diagram,regions IV, V, VI, and VII represent the set Candregions II, III, V, and VI represent the set B.
Now, the union of the regions of A and Bthatare II, III, IV, V, VI, and VII represent the set\[B\cup C\].
Now, find the intersection of the set \[B\cup C\] and set A.
Common regions of both the sets together represent the set\[A\cap \left( B\cup C \right)\].
So, regions II, IV, and V represent the set\[A\cap \left( B\cup C \right)\].
(b)
First, perform the operation inside the parentheses of the set\[A\cup \left( B\cap C \right)\].
In the provided Venn diagram,regions I, II, IV, and V represent the set A,regions II, III, V, and VI represent the set B,andregions IV, VI, VI, and VII represent the set C.
Now, find set\[B\cap C\].
Common regions of the sets B and C are V and VI together represent the set\[B\cap C\].
Now, the union of regions of the set A and set\[B\cap C\] are I, II, IV, V, and VI,and together they represent the set\[A\cup \left( B\cap C \right)\].
(c)
In part (a),the set \[A\cap \left( B\cup C \right)\]is represented by the regions II, IV, and V, and in part(b), set \[A\cup \left( B\cap C \right)\]is represented by regions I, II, IV, V, and VI.
Both the sets are represented bydifferent regions,so they are not equal.
Work Step by Step
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