Which of the following represent the distributive law in sets?

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

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

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

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

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Solution

The correct options are
B $A \cap (B \cup C) = (A \cap B) \cup (A \cap C)$
D $A \cup (B \cap C) = (A \cup B) \cap (A \cup C)$
Distributive law in sets.
$A \cap (B \cup C) = (A \cap B) \cup (A \cap C)$
$A \cup (B \cap C) = (A \cup B) \cap (A \cup C)$

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Similar questions

(Distributive laws) For any three sets A, B, C prove that:

I. $A \cup (B \cap C) = (A \cup B) \cap (A \cup C)$
[Distirbutive law of union over intersection]

II. $A \cap [(B \cup C)] = (A \cap B) \cup (A \cap C)$
[Distributive law of intersection over union]

(A + B) . (A + C) = (A + B) . C

A = {a, b, c}

A = {a, b, c} :

R_{1} = {(c, a), (b, b), (a, c), (c, c), (b, c), (a, a)}

R_{2} = {(a, b), (b, a), (c, c), (c, a), (a, a), (b, b), (a, 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.

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