Answer:
a. closed under addition and multiplication
b. not closed under addition but closed under multiplication.
c. not closed under addition and multiplication
d. closed under addition and multiplication
e. not closed under addition but closed under multiplication
Step-by-step explanation:
a.
Let A be a set of all integers divisible by 5.
Let
∈A such that ![x=5m\,,\,y=5n](https://tex.z-dn.net/?f=x%3D5m%5C%2C%2C%5C%2Cy%3D5n)
Find ![x+y,xy](https://tex.z-dn.net/?f=x%2By%2Cxy)
![x+y=5m+5n=5(m+n)](https://tex.z-dn.net/?f=x%2By%3D5m%2B5n%3D5%28m%2Bn%29)
So,
is divisible by 5.
![xy=(5m)(5n)=25mn=5(5mn)](https://tex.z-dn.net/?f=xy%3D%285m%29%285n%29%3D25mn%3D5%285mn%29)
So,
is divisible by 5.
Therefore, A is closed under addition and multiplication.
b.
Let A = { 2n +1 | n ∈ Z}
Let
∈A such that
where m, n ∈ Z.
Find ![x+y,xy](https://tex.z-dn.net/?f=x%2By%2Cxy)
![x+y=2m+1+2n+1=2m+2n+2=2(m+n+1)](https://tex.z-dn.net/?f=x%2By%3D2m%2B1%2B2n%2B1%3D2m%2B2n%2B2%3D2%28m%2Bn%2B1%29)
So,
∉ A
![xy=(2m+1)(2n+1)=4mn+2m+2n+1=2(2mn+m+n)+1](https://tex.z-dn.net/?f=xy%3D%282m%2B1%29%282n%2B1%29%3D4mn%2B2m%2B2n%2B1%3D2%282mn%2Bm%2Bn%29%2B1)
So,
∈ A
Therefore, A is not closed under addition but A is closed under multiplication.
c.
![Let A=\{2,5,8,11,14,...\}](https://tex.z-dn.net/?f=Let%20A%3D%5C%7B2%2C5%2C8%2C11%2C14%2C...%5C%7D)
Let
but
∉A
Also,
∉A
Therefore, A is not closed under addition and multiplication.
d.
Let A = { 17n: n∈Z}
Let
∈ A such that ![x=17n,y=17m](https://tex.z-dn.net/?f=x%3D17n%2Cy%3D17m)
Find x + y and xy
![x+y=17n+17m=17(n+m)](https://tex.z-dn.net/?f=x%2By%3D17n%2B17m%3D17%28n%2Bm%29)
![xy=(17m)(17n)=289mn=17(17mn)](https://tex.z-dn.net/?f=xy%3D%2817m%29%2817n%29%3D289mn%3D17%2817mn%29)
So,
∈ A
Therefore, A is closed under addition and multiplication.
e.
Let A be the set of nonzero real numbers.
Let
∈ A such that ![x=-1,y=1](https://tex.z-dn.net/?f=x%3D-1%2Cy%3D1)
Find x + y
![x+y=-1+1=0](https://tex.z-dn.net/?f=x%2By%3D-1%2B1%3D0)
So,
∈ A
Also, if x and y are two nonzero real numbers then xy is also a non-zero real number.
Therefore, A is not closed under addition but A is closed under multiplication.
Answer:
5/11
Step-by-step explanation:
5 blue marbles and 11 total marbles
The answer would be D because an indulgence is when you pay to forgive your sin
Answer:
true
Step-by-step explenation:
follow order of operations
5 -8/2 = 5 - (8/2)= 5-4= 1
<span>one way to solve this kind of problems is by doing a little bit of reversal
75 % * X = 54
75/100 * X = 54
(we move 75/100 to the right, since it's a fraction the top and bottom number will be reversed)
X = 54 * 100/75
X = 5400 / 75
X = 72 Hope I helped! :) Cheers!</span>