Which of the following correctly explains distributive law-All of these-a -b-c- - b - a - a - c-b - nbsp-a-c- - b - nbsp-a - b - nbsp-c-a-c- - nbsp-b - a - b nbsp- c - b-

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Distributivity

Which of the ...

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Which of the following correctly explains distributive law?

$a \times (b + c) = b \times a + a \times c$

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$b \times (a + c) = b \times a + b \times c$

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$(a + c) \times b = a \times b + c \times b$

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All of these

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

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

A \cup (B - C) = (A \cup B) \cap (A \cup C')

A \cup (B - C) = (A \cup B) - (A \cup C) .

(a) If A = {1, 3, 4, 8, 9, 12}, B = {1, 4, 9} and C = {2, 4, 8, 10}

Find (i) A ∪ (B ∩ C) (ii) A ∩ (B ∪ C) (iii) (A ∪ B) ∩ (A ∪ C) (iv) (A ∩ B) ∪ (A ∩ C)

(b) If A = (2, 4, 6, 8, 10}, B = {1, 2, 3, 4, 5, 6} and C = (1, 3, 5, 7, 9, 11, 13}

Verify (i) A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) (ii) A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

(iii) (A ∩ B) ∪ C = (A ∪ C) ∩ (B ∪ C) (iv) (A ∪ B) ∩ C = (A ∩ C) ∪ (B ∩ C)

Y = {x : x is an even number less than 12}

Z = {x : x is an odd number less than 12}

Show that (i) union of sets of distributive over intersection of sets.

(ii) intersection of sets is distributive over union of sets.

|\begin{matrix} a + b + c & - c & - b \\ - c & a + b + c & - a \\ - b & - a & a + b + c \end{matrix}| = 2 (a + b) (b + c) (c + a)

∣ ∣ ∣ ∣ ∣ \begin{matrix} b c - a^{2} & c a - b^{2} & a b - c^{2} - b c + c a + c b & b c - c a + a b & b c + c a - a b (a + b) (a + c) & (b + c) (b + a) & (c + a) (c + b) \end{matrix} ∣ ∣ ∣ ∣ ∣ = 3 (b - c) (c - a) (a - b) (a + b + c) (b c + c a + a b)

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