If two sets A and B have 99 elements in common, then the number

1.	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
Answer» To 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

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

Answer»

To 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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