Question

If $ A = \left\{ {2,4,5} \right\} $ and $ B = \left\{ {7,8,9} \right\} $ then $ n(A \times B) $ is equal to
A. $ 6 $
B. $ 9 $
C. $ 3 $
D. $ 0 $

Answer 1

Hint: In this question we have two sets. We have to find the value of $ n(A \times B) $ . We will apply the formula of multiplication of sets i.e. $ n(A \times B) = n(A) \times n(B) $ , where $ n(A) $ is the number of elements in set A and $ n(B) $ represents the number of elements in set B. We will first find these two values and then multiply them.

Complete step by step solution:
We have first set:
 $ A = \left\{ {2,4,5} \right\} $
We can see that there are total three elements in set A , so it gives
 $ n(A) = 3 $
Now we have the second set which is;
 $ B = \left\{ {7,8,9} \right\} $
In the above set, we can see that here also only three elements are present in set B. Therefore,
 $ n(B) = 3 $ .
Now we apply the formula :
 $ n(A \times B) = n(A) \times n(B) $
By putting the value in the formula we have:
 $ n(A \times B) = 3 \times 3 $
So it gives the value,
 $ n(A \times B) = 9 $
Hence the correct option is (B)
So, the correct answer is “Option B”.

Note: We can also cross check our answer by the Cartesian product of two sets. The Cartesian product of two sets A and B denoted by $ A \times B $ , is the set of all the possible ordered pairs where the elements of A are first and the elements of B are second. So from the above question, we can write $ n(A \times B) = \left\{ {(2,7),(2,8)(2,9),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9)} \right\} $ .
We can see that there are total $ 9 $ elements in the product of both the sets. Hence our answer is correct.