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Definition of Sets

Verify the fo...

Question

Verify the following identities where A = {1, 2, 3, 4, 5}, B = {2, 3, 5, 6}, C = {4, 5, 6, 7}
$A \cap (B \cup C) = (A \cap B) \cup (A \cap C)$

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Solution

A{ $1, 2, 3, 4, 5$ }

B{ $2, 3, 5, 6$ }

C{ $4, 5, 6, 7$ }

$(B \cup C) = 2, 3, 4, 5, 6, 7$

$A \cap (B \cup C) = 2, 3, 4, 5$ ...(1)

$(A \cap B) = 2, 3, 5$

$(A \cap C) = 4, 5$

$(A \cap B) \cup (A \cap C) = 2, 3, 4, 5$ ...(2)

From (1) and (2)

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

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