Question

Which sets of numbers are closed under multiplication?

Choose all answers that are correct.

A.
whole numbers

B.
natural numbers

C.
negative integers

D.
integers

Answer 1

@SolomonZelman

Answer 2

@iGreen

Answer 3

what it means to be closed under a multiplication is that if you multiply, let set even number times an even number you get an even number:

\(\large\color{royalblue}{ {\rm even} ~\times~{\rm even}~=~\color{blueviolet}{{\rm even}} }\) (hence \(\normalsize\color{royalblue}{\color{blue}{{\rm even}} }\) is closed under multiplication)

Answer 4

but, a counterexample, (saying that not every set is closed under multiplication) would be:

\(\large\color{royalblue}{ ({\rm prime~number}) ~\times~({\rm prime~number})~\ne~\color{blueviolet}{{\rm {\rm prime~number}}} }\)

because,

\(\large\color{royalblue}{ ({\rm prime~number}) ~\times~({\rm prime~number})~=~\color{blueviolet}{{\rm {\rm composite~number}}} }\)

Answer 5

that means that prime numbers are NOT closed under multiplication

Answer 6

C and D?

Answer 7

lets retry this

Answer 8

im runing out of time for this test im doing please hurry :'(

Answer 9

Tell me if each statement is (always) true or not:

\(\large\color{teal}{ ({\rm whole~number}) ~\times~({\rm whole~ number})~=~\color{blueviolet}{{\rm whole~number}} }\)

\(\large\color{teal}{ ({\rm natural~number}) ~\times~({\rm natural~ number})~=~\color{blueviolet}{{\rm natural~number}} }\)

\(\large\color{teal}{ ({\rm negative~number}) ~\times~({\rm negative ~ number})~=~\color{blueviolet}{{\rm natural~number}} }\)

\(\large\color{teal}{ ({\rm integer}) ~\times~({\rm integer})~=~\color{blueviolet}{{\rm integer }} }\)

Answer 10

so its a and b?

Answer 11

yes, but there is one more correct answer choice

Answer 12

d?

Answer 13

yup

Answer 14

A, B & D.

Answer 15

ok thank u!! :3

Answer 16

yw

Answer 17

messed up on the 3rd statement, but you got the idea... yw