Question

Is the set of multiples of 4 closed under addition? Explain why or provide a counterexample if not.

A.
Yes, because the sum of any two multiples of 4 is also a multiple of 4.

B.
Yes, because the sum of any two multiples of 4 is also a multiple of 8.

C.
No, and a counterexample is –4 + (–8) = –12.

D.
No, and a counterexample is 26 + 16 = 42.

Answer 1

@geerky42

Answer 2

well let's look at these "counterexamples" and see if they are actual counterexamples

Answer 3

are 4 and 8 multiples of 4?

Answer 4

yup

Answer 5

4 times two 8

Answer 6

is the the sum of -4+(-8) a multiple of 4?

Answer 7

that is is -12 a multiple of 4?

Answer 8

umm...

Answer 9

no?

Answer 10

4 times 3 is 12
so -12 is a multiple of 4

Answer 11

oh XD im not that smart

Answer 12

so this is definitely not an example showing the multiples of 4 aren't closed under addition

Answer 13

kk

Answer 14

so lets look at the other counterexample

Answer 15

okay

Answer 16

is 26 a multiple of 4/

Answer 17

no?

Answer 18

so we need to go no further there
we definitely know that can not be a choice then

Answer 19

so the answer has to be yes

Answer 20

do you think it is A or B and why

Answer 21

4k+4k=8k=4(2k) where k is an integer

Answer 22

whats an integer

Answer 23

integer={...,-3,-2,-1,0,1,2,3,....,100,...100000,....}

Answer 24

dont get it.

Answer 25

an integer is a whole number so 1,2 3, or -1,-2 or -3
1/2 or 1.55 are not integers so fractions and decimals are NOT and integer

Answer 26

oh ok

Answer 27

also I would probably write 4L+4K=4(L+K)
where L+K is an integer

Answer 28

since K and L are integers

Answer 29

ohhh ya sorryyy . Forgot to take that into consideration

Answer 30

Ok so basically when you add two integers that are multiples of 4 the sum is a multiple of 4

Answer 31

so a?

Answer 32

lol yaaa -.-

Answer 33

thx

Answer 34

you're awesome @swissgirl

Answer 35

Not really sure abt that @freckles is the awesome one

Answer 36

you're both awesome!