Question

if A={1,2,3,4} then the number of elements in A×A is

Answer 1

A×A={(1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (4,4)}

Answer 2

Answer:

There are 16 elements in the set A×A

Step-by-step explanation:

Given set A={1, 2, 3, 4}

we have to find the number of elements in A×A

For two sets A and B, the Cartesian product A × B is set of all ordered pairs  (a, b) where a ∈ A and b ∈ B.

The number of elements in the set is the cardinality of that set.

The cardinality of resulting set is equal to the product of the cardinalities of all the input sets i.e   |A × B| = |A| · |B|

As set A has 4 elements therefore the number of elements is

$|A\times A|=|A|.|A|=4\times 4=16$

Hence, there are 16 elements in the set A×A