Five marks example problems III — task. Mathematics State Board, Class 10.

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Let

$A = \{x \in \mathbb{N}|1 < x < 4\}$ ,

$B = \{x \in \mathbb{W}|0 \leq x < 2\}$ and

$C = \{x \in \mathbb{N}|x < 3\}$ . Then verify that

$A \times (B \cap C) = (A \times B) \cap (A \times C)$

Answer:

To prove:

$A \times (B \cap C) = (A \times B) \cap (A \times C)$

Explanation:

$B \cap C = \{$

$\}$

$A \times (B \cap C) = \{$

$\}$

$A \times B = \{$

$\}$

$A \times C = \{$

$\}$

$(A \times B) \cap (A \times C) =\{$

$\}$

As a result,

$A \times (B \cap C) = (A \times B) \cap (A \times C)$

Hence, we proved.

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11. Five marks example problems III