Question

Which of the following gives an example of a set that is closed under multiplication?

The product of an even number and an even number

The product of a prime number and a prime number.

The product of a negative number and a negative number

The product of a perfect cube and a perfect cube

Answer 1

Wow what grade are you in? Why are you asking both very basic questions and very advanced questions?

Answer 2

lol that was my question

Answer 3

Look at what happens when you multiply two numbers of the given type, do you get back a number of the given type?

Answer 4

A set that is closed under multiplication means that when two elements of the set are multiplied together, it still gives you element of that set

Answer 5

what is whole number*whole number?

Answer 6

Depends on the book's definition of "whole number", it's not universally defined. It's often defined as the nonnegatve integers, i.e. the counting numbers + 0

Answer 7

Do you get an even number when you multiply two even numbers together?
Do you get a prime number when you multiply two prime numbers together?
Do you get a negative number when you multiply two negative numbers together?
Do you get a perfect cubes when you multiply two perfect cubes together?

Answer 8

the first one does not make sense
the second one is closed 0*0=0 which is in {0}
the third one is closed because whole number*whole number = whole number is in {whole numbers}
the third one does not make sense

Answer 9

What do you mean, the first one does not make sense?

Answer 10

@shelbygt520 the first one is correct, the second is not closed, the third is not closed, the fourth is also not closed

Answer 11

C, the 4th is cclosed

Answer 12

KC, even

Answer 13

Even number times even number = even number
prime number times prime number = composite number
negative number times negative number = positive number
perfect cube times perfect cube = non perfect cube

Answer 14

Wrong, kc, here's the explanation

Answer 15

yeah my bad typing the 4th is closed the third is closed ands is the second

Answer 16

ok let farabor defend himself

Answer 17

no your going to be in that position soon lol

Answer 18

i know @shelbygt520 xD

Answer 19

Let a and b be perfect cubes. Then there exists numbers x and y such that
\[a=x^3,b=y^3\].
Then ab=\[x^3y^3=(xy)^3\]

Answer 20

oh sorry my careless mistake, so A and D are both correct?

Answer 21

yep

Answer 22

Yep. Same logic applies to why 2 even numbers form an even number

Answer 23

@kc_kennylau I'm in 11th grade.

Answer 24

Did you follow hte reasons why those two are closed, and b and c are not closed?

Answer 25

@Trojan you are learning basic maths like pemdas in 11th grade? or actually two people are using the same account?

Answer 26

No, I'm the only one using Trojan.

Answer 27

hell I learned PEMDAS in 7th grade

Answer 28

@shelbygt520 wow

Answer 29

whats so wow lol

Answer 30

@kc_kennylau @shelbygt520 Relax, the person probably just had a few pints.

Answer 31

haha good one

Answer 32

@Trojan I recommend you start go over the little things; in 11th grade you should know much more than some of the stuff you were asking. We're all just looking out for you.

Answer 33

can we switch back to the topic, @Trojan do you follow why the answer is A and D?

Answer 34

I don't know why I said wow. I mean it does seem like a low grade level thing. I really don't understand why I'm doing half of the math things I'm doing now. Last grade I was doing calculus.

Answer 35

@kc_kennylau Yes I understand why it's A and D.

Answer 36

ok then why are you doing Pre-Algebra now lol

Answer 37

Maybe it's the teacher who had too much to drink.

Answer 38

@shelbygt520 No clue. I shorta hate my school. Can't wait till I go back to New York so I can attend a real school.

Answer 39

yeah @Trojan you should ask her if she had a bit to much tequila

Answer 40

@Trojan if you understand, may you please kindly close the question :)

Answer 41

@kc_kennylau Sure :)

Answer 42

Come on, this is math section, we should be asking questions such as 2+2=? here, not discussing your life

Answer 43

where are you living now?

Answer 44

2+2=0, in a field with characteristic 4 :)

Answer 45

@kc_kennylau Calm your teats; one's life can affect how one perceives math. We also help morally too. Plus school sucks anyways.

Answer 46

@primeralph ok :)

Answer 47

yeah SCHOOL SUCKS ill toast to that XD

Answer 48

@shelbygt520 Waterloo, IA

Answer 49

when you come out to work you'll miss school

Answer 50

Anyhow, should probably move the chatter to the chat channel and outside of a topic question so those of us following other things don't keep getting spammed with new messages here :) (Hint hint)

Answer 51

@farabor can't agree more :D

Answer 52

not really my job is going to be shooting people and finding serial killers that doesn't define OMG I MISS YOU SCHOOL PLSSS LET ME BACK!

Answer 53

lolz @shelbygt520 bye gotta help more ppl