Number of elements of A × B = Number of Elements of A  ×  Number of elements of B

 

So, if set A has 3 elements, set B has 2 elements

Number of elements of A × B = 3 × 2 = 6

 

Let us check

If A = {1, 2, 3}, B = {3, 4}

A  × B = {(1, 3), (1, 4),

        (2, 3), (2, 4),

        (3, 3), (3, 4)}

Number of elements of A × B = 6

 

If A × A has 9 elements, then how many elements does set A have?

We know that

Number of elements of A × A = Number of Elements of A  ×  Number of elements of A

Number of elements of A × A = (Number of elements of A) 2

9 = (Number of elements of A) 2

(Number of elements of A) 2 = 9

Number of elements of A = √9 = 3

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.