Problem

For $P=\{11,12,14,15\}, Q=\{1,7,13\}$, and $R=\{3,7,10,13\}$, find $P \cup(Q \cap R)$. The answer is (Use a comma to separate answers as needed.)

Solution

Step 1 :Given sets are: \(P = \{11, 12, 14, 15\}\), \(Q = \{1, 7, 13\}\), and \(R = \{3, 7, 10, 13\}\).

Step 2 :Find the intersection of sets Q and R. The intersection of two sets is the set of elements which are common to both sets. So, \(Q \cap R = \{7, 13\}\).

Step 3 :Find the union of set P and the intersection of sets Q and R. The union of two sets is the set of elements which are in either set. So, \(P \cup (Q \cap R) = \{7, 11, 12, 13, 14, 15\}\).

Step 4 :\(\boxed{P \cup (Q \cap R) = \{7, 11, 12, 13, 14, 15\}}\)

From Solvely APP
Source: https://solvelyapp.com/problems/31266/

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