Question

Which sets of numbers are closed under addition?

Choose all answers that are correct.

A.
{0, 2, 5, 8}

B.
even integers

C.
rational numbers

D.
{0}

Answer 1

@PyroYolka @Ilovecake

Answer 2

k well closed under addition means that when you add any of the values stated in that set the sum will still be in that set

For instance lets begin with A
{0,2,5,8}
0+2=2 Since 2 is in the set we can still assume its closed under addition
2+5=7 Is 7 in the set of {0,2,5,8}
Obviously notttttt sooo therefore we can conclude that this set is NOT closed under addition

Answer 3

Now lets look at the second option

All even integers
Even integers can be represented as 2k where k is an integer
Now lets add 2 integers
2l+2m where l and m are both integers
2l+2m=2(l+m) where l and m are integers
Therefore we can conclude that when adding even integers it will always result in an even integer. Hence it is closed under addition

Answer 4

@Thebadyboy Do you follow so far?

Answer 5

yes

Answer 6

Lets go to the third option which is rational numbers
Rational numbers is a real number that can be written as a fraction
Rational numbers can be represented as \(\frac{p}{q}\) where p and q are integers
Now lets add 2 rational numbers
\(\frac{a}{b}+\frac{c}{d}\) where a,b,c and d are integers

\(\frac{a}{b}+\frac{c}{d}=\frac{ad+cb}{bd}\)
Since a,b, c and d are integers we can conclude that \(\frac{ad+cb}{bd}\) is a rational number
Hence it is closed under addition

Answer 7

that makes sence

Answer 8

Now the last option is pretty obvious
The set only containing 0
0+0=0
Hence .... It is closed under addition

Answer 9

thx

Answer 10

not sure what grade you are in but if you didnt understand the second and third option I can explain it in simpler terms

Answer 11

thx i understand

Answer 12

Numbers p and q are positive integers.

Which statements are always true?

Choose all answers that are correct.

A.
p + q is a positive integer

B.
p – q is a negative integer

C.
p • q is a positive integer

D.
p/q is a positive integer

Answer 13

can u answer this one plz

Answer 14

Lol can u attempt to answer this ... ill guide u

Answer 15

ok