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If a = {2, 3}, B = {4, 5}, C ={5, 6}, Find a × (B ∪ C), a × (B ∩ C), (A × B) ∪ (A × C). - Mathematics

If A = {2, 3}, B = {4, 5}, C ={5, 6}, find A × (B ∪ C), A × (B ∩ C), (A × B) ∪ (A × C).

 
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Solution

Given:
A = {2, 3}, B = {4, 5} and C ={5, 6}
Also,
(B ∪ C) = {4, 5, 6}
Thus, we have:
A × (B ∪ C) = {(2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3,6)}
And,
(B ∩ C) = {5}
Thus, we have:
A × (B ∩ C) = {(2, 5), (3, 5)}
Now,
(A × B) = {(2, 4), (2, 5), (3, 4), (3, 5)}
(A × C) = {(2, 5), (2, 6), (3, 5), (3, 6)}
∴ (A × B) ∪ (A × C) = {(2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6)}

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 2 Relations
Exercise 2.2 | Q 2 | Page 12
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