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Distributive Property

A=5,7,9,11,13...

Question

$A = {5, 7, 9, 11, 13, 15)$ and $B = {7, 8, 11, 15, 20}$ and $C = {5, 8, 9, 11, 13, 15, 17, 20}$ verify that : $A \cap (B \cap C) = (A \cap B) \cap C$

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Solution

$∵ B \cap C = {8, 11, 15, 20} a n d, A \cap (B \cap C) = {11.15} ⟶ (1) a l s o, A \cap B = {7, 11, 15} a n d (A \cap B) \cap C = {11, 15} ⟶ (2) f r o m (1) a n d (2) i t i s v e r i f i e d t h a t A \cap (B \cap C) = (A \cap B) \cap C$

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Let $A = {1, 2}, B = {3, 4}$ and $C = {4, 5}$ . Verify that $(A \times B) \times C = A \times (B \times C)$ and hence find $A \times B \times C$

a = - 8, b = - 7

c = 6

(a + b) + c = a + (b + c)

= {1, 2, 3, 4}

= {3, 4, 5, 6}

= {6, 7}

\cap

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A = {1, 2}, B = {1, 2, 3, 4}

C = {5, 6}

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

A = {a, b}, B = {x, y}

C = {a, c, y}

A \times (B \cup C) = (A \times B) \cup (A \times C)

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