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Question

If A={5,7},B={7,9} and C={7,9,11}, find :
Whether A×(BC)=(A×B)(A×C) holds true or not?

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Solution

Union of two sets has all the elements of both the sets
=>BC= { 7,9,11 }
Product of two sets is the set of ordered pairs formed by mapping every element from the first set to every element of the second set.
So, A×(BC)= { (5,7),(5,9),(5,11),(7,7),(7,9),(7,11) }
Also,
And A×B= { (5,7),(5,9),(7,7),(7,9) }
Now, A×C= { (5,7),(5,9),(5,11),(7,7),(7,9),(7,11) }
And, (A×B)(A×C)= { (5,7),(5,9),(5,11),(7,7),(7,9),(7,11) }
Hence, A×(BC)=(A×B)(A×C) holds true

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