Question

Group Lifesaver
Hi again! i need your help again. please give me some examples for the closure property in this set:
The set of prime numbers is closed under multiplication.

Answer 1

Question: If I take two prime numbers and multiply them together - is the output another prime number?

Answer 2

What's 3*7?

Answer 3

You were given the definition of a prime number yesterday, don't you remember?

Answer 4

my friend delete it!!

Answer 5

A prime number is a number that is only divisible by 1 and itself.

Answer 6

uhm. example? i'm confuse

Answer 7

So. Take two prime numbers, say 3 and 7; multiply them together, and tell me what you get.

Answer 8

21

Answer 9

Ok. Good. Now, is 21 only divisible by 1 and 21?

Answer 10

no

Answer 11

Good. Also correct. So is the set of prime numbers closed under multiplication?

Answer 12

i think so?

Answer 13

What does "closed" mean?

Answer 14

No. To be closed under multiplication would mean that when you multiplied two prime numbers together you got another prime number; which you just proved you don't.

Answer 15

Closure is a reference to a set property.

Answer 16

oh now i get it! yea ur right

Answer 17

I know what closed means I was asking the op.

Answer 18

It's also not closed under addition. (i.e. 3+7 = 10, and 10 is not prime)

My bad estudier.

Answer 19

Just to be pedantic, 1 is not a prime even though it is divisible by itself and 1.