The range is the difference between the LOWEST value and the HIGHEST value.
The range is the set of POSSIBLE output values, and that is shown on the Y-AXIS!!
Answer:
I thinks they take 5 hours to meet each other
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.
BD=10 because it is symmetrical to AD.