Question

# If two sets A and B have 99 elements in common, then the number of elements common to each of the sets A×B and B×A are

A
299
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B
992
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C
100
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D
18
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Solution

## The correct option is B 992To find A×B we take one element from set A and one from set B. Given that 99 elements are common to both set A and set B.Suppose these common elements are N1,N2,N3,...N99. Select an ordered pair for A×B such that both are selected out of these common elements. Examples: (N1,N2),(N3,N5)All these will also be elements of B×A. Hence number of elements common to A×B and B×A is 99×99=992 ( first element in ordered pair can be selected in 99 ways; second element can also be selected in 99 ways)n[(A×B)∩(B×A)]=n[(A∩B)∩(B∩A)]=(99)(99)=992

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