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If $A=\{x: x \in W, x < 2\}, B=\{x: x \in N, 1 < x < 5\}$ and $C=\{3,5\}$, then find.
(i) $A \times(B \cap C)$
(ii) $A \times(B \cup C)$
(i) $A \times(B \cap C)$
(ii) $A \times(B \cup C)$
Solution:
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Verified Answer
We have, $A=\{x: x \in W, x < 2\}=\{0,1\}$
and $B=\{x: x \in N, 1 < x < 5)=\{2,3,4)$
and $C=\{3,5\}$
(i) Since $B \cap C=\{3\}$
$\therefore \quad A \times(B \cap C)=\{0,1\} \times\{3\}=\{(0,3),(1,3)\}$
(ii) $\because(B \cup C)=\{2,3,4,5\}$
$\therefore \quad A \times(B \cup C)=\{0,1\} \times\{2,3,4,5\}$
$=\{0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)\}$
and $B=\{x: x \in N, 1 < x < 5)=\{2,3,4)$
and $C=\{3,5\}$
(i) Since $B \cap C=\{3\}$
$\therefore \quad A \times(B \cap C)=\{0,1\} \times\{3\}=\{(0,3),(1,3)\}$
(ii) $\because(B \cup C)=\{2,3,4,5\}$
$\therefore \quad A \times(B \cup C)=\{0,1\} \times\{2,3,4,5\}$
$=\{0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)\}$
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