Question

If $ n(A) = 2 $ and $ B = \{ - 1,0,3\} $ then what is the number of elements of $ A \times B $

Answer 1

Hint: The number of elements in $ A \times B $ is the product of the number of elements in A and the number of elements in B. Here we are given number of elements in A and the set B. for the elements in set B count the number of elements and then find the product for the resultant required answer.

Complete step by step solution:
Given that: Number of elements in A, $ n(A) = 2 $ …. (I)
And the set $ B = \{ - 1,0,3\} $
Number of elements in B, $ n(B) = 3 $ …. (II)
Now, the number of elements in $ A \times B = n(A) \times n(B) $
By using the equations (I) and (II), place the values in the above equation
 $ n(A \times B) = 2 \times 3 $
Simplify the above equation and find the product of the equation on the right hand side of the above equation.
 $ n(A \times B) = 6 $
This is the required solution.
So, the correct answer is “6”.

Note: Be good in multiples and find the factors, remember multiples of the numbers at least till twenty for the efficient and the accurate solution. Remember the set can be defined as the collection of the distinct objects or the elements which have common property. Here we were given the set in the roster form in case it is not converted to all the given set in the roster form where the elements of a set are listed and separated by commas. Follow the given conditions properly while converting the set-builder to roster form. Set builder notation is used to describe a set by enumerating the elements or stating the properties to satisfy for its members.