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If $P=\{x: x < 3, x \in N\}, Q=\{x: x \leq 2, x \in W\}$, then find
$(P \cup Q) \times(P \cap Q)$, where $W$ is the set of whole numbers.
$(P \cup Q) \times(P \cap Q)$, where $W$ is the set of whole numbers.
Solution:
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Verified Answer
We have, $P=\{x: x < 3, x \in N\}=\{1,2\}$
and $Q=\{x: x \leq 2, x \in W\}=\{0,1,2\}$
$\therefore \quad P \cup Q=\{0,1,2\}$ and $P \cap Q=\{1,2\}$
$(P \cup Q) \times(P \cap Q)=\{0,1,2\} \times\{1,2\}$
$=\{(0,1),(0,2),(1,1),(1,2),(2,1),(2,2)$
and $Q=\{x: x \leq 2, x \in W\}=\{0,1,2\}$
$\therefore \quad P \cup Q=\{0,1,2\}$ and $P \cap Q=\{1,2\}$
$(P \cup Q) \times(P \cap Q)=\{0,1,2\} \times\{1,2\}$
$=\{(0,1),(0,2),(1,1),(1,2),(2,1),(2,2)$
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