Question

Which of the following gives an example of a set that is closed under multiplication? Choose all that apply. The product of a prime number and a prime number The product of an odd number and an odd number The product of a negative number and a negative number The product of a positive number and a positive number

Answer 1

the product of a prime number and a prime number


The product of an odd number and an odd number

Answer 2

The examples which shows that a set is closed under multiplication is:

• The product of a odd number and a odd number.

• The product of a positive number and a positive number.

Explanation:

A set "P" is closed under multiplication means :

If a,b∈P

Then ab∈P

a)

The product of a prime number and a prime number.

This set is not closed under multiplication.

Because 2,3 both belongs to the set of prime numbers.

But 2×3=6 is not a prime number.

b)

The product of an odd number and an odd number .

This set is closed under multiplication.

Since multiplication of two odd numbers is always a odd number.

c)

The product of a negative number and a negative number.

This set is not closed under multiplication.

Since the product of 2 negative numbers is always a positive number.

d)

The product of a positive number and a positive number.

This set is closed under multiplication.

Since the product of 2 positive numbers is always a positive number.