Answer:
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.
Step-by-step 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.
