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Llana [10]
3 years ago
6

Help 1-4 please 94 points

Mathematics
2 answers:
AlekseyPX3 years ago
8 0

Hello!

1) 2

2) 3

3) 6

4) 6

I hope it helps!

Mice21 [21]3 years ago
7 0
Q1=2 because .5+.5+.5+.5=2
Q2=3 because 3/4 times 4=3
Q3=6 because all of the 1/4 added together =1 plus Q1 and Q2=6
Q4=6 divided by the ammout of bags.
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i think its C

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Let A be a set of numbers.
LUCKY_DIMON [66]

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 x,y∈A such that x=5m\,,\,y=5n

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x+y=5m+5n=5(m+n)

So, x+y is divisible by 5.

xy=(5m)(5n)=25mn=5(5mn)

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xy is divisible by 5.

Therefore, A is closed under addition and multiplication.

b.

Let  A = { 2n +1 | n ∈ Z}

Let x,y∈A such that x=2m+1\,,\,y=2n+1 where m, n ∈ Z.

Find x+y,xy

x+y=2m+1+2n+1=2m+2n+2=2(m+n+1)

So,

x+y ∉ A

xy=(2m+1)(2n+1)=4mn+2m+2n+1=2(2mn+m+n)+1

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xy∈ A

Therefore, A is not closed under addition but A is closed under multiplication.

c.

Let A=\{2,5,8,11,14,...\}

Let x=2,y=5 but x+y=2+5=7∉A

Also,

xy=2(5)=10∉A

Therefore, A is not closed under addition and multiplication.

d.

Let A = { 17n: n∈Z}

Let x,y ∈ A such that x=17n,y=17m

Find x + y and xy

x+y=17n+17m=17(n+m)

xy=(17m)(17n)=289mn=17(17mn)

So,

x+y,xy ∈ A

Therefore, A is closed under addition and multiplication.

e.

Let A be the set of nonzero real numbers.

Let x,y ∈ A such that x=-1,y=1

Find x + y

x+y=-1+1=0

So,

x+y ∈ 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.

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