annie12m
  • annie12m
Is the set of numbers that can be written as the product of 6 and an integer closed under subtraction? A. Yes, because the difference of any two multiples of 6 is equal to 6. B. Yes, because the difference of any two multiples of 6 is also a multiple of 6. C. No, and a counterexample is 6 – 6 = 0. D. No, and a counterexample is 6 – 18 = –12.
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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annie12m
  • annie12m
please help
anonymous
  • anonymous
C and D are out right? since both 0 and -12 are multiples of 6
jchick
  • jchick
We need to get an understanding of what these number look like. >Is the set of numbers that can be written as the product of 6 and an integer closed The integers are {...-3, -2, -1. 0, 1, 2, 3, ...}

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jchick
  • jchick
6 times each of those would be: {..., -18, -12, -6, 0, 6, 12, 18, ...}
jchick
  • jchick
any two of those numbers and subtract them, will you get an answer that is also in that set.
jchick
  • jchick
6-6 = 0
jchick
  • jchick
the difference of any two multiples of 6 is equal to 6. 12 is a multiple of 6 24 is a multiple of 6. 12 - 24 is not equal to 6. So, throw out option A. It is wrong.
jchick
  • jchick
6 - 6 = 0 which is a multiple of 6 because 0 times 6 = 0. So, throw out option C.
jchick
  • jchick
6 - 18 = -12 but -12 is a multiple of 6 because 6 times -2 = -12. Throw out option D
jchick
  • jchick
The answer is B because the difference of any two multiples of 6 is also a multiple of 6.
annie12m
  • annie12m
so its ethier one of the yeses
annie12m
  • annie12m
oh ok thanks
jchick
  • jchick
Well we eliminated A, C, and D
jchick
  • jchick
So that only left B
jchick
  • jchick
No problem!
annie12m
  • annie12m
can you help me with 4 more questions?
jchick
  • jchick
Yes
annie12m
  • annie12m
ok ill give you one at a time
jchick
  • jchick
Ok thanks!
annie12m
  • annie12m
Numbers p and q are negative integers. Which statements are true? Choose all that are correct. A. p + q is a negative integer B. p • q is a positive integer C. p – q is a negative integer D. p/ q is a negative integer
annie12m
  • annie12m
A is correct? B is wrong? C not sure. D is wrong?
annie12m
  • annie12m
jckick you there?
jchick
  • jchick
let's assign p and q numbers p=3 and q=5
jchick
  • jchick
Yes
jchick
  • jchick
is 3+5 an integer? 3-5? 3*5? 3÷5?
annie12m
  • annie12m
well it said p and q are both going to negative
jchick
  • jchick
A. p + q is a positive integer TRUE! Two positive numbers added = a positive number! Always! B. p – q is a negative integer Maybe not. Ie if P = 10 and q = 1, p-q = 10-1 = +9. FALSE C. p • q is a positive integer Yes. Two positive numbers multiplied together is still a positive integer D. is a positive integer
annie12m
  • annie12m
so a and c are correct?
jchick
  • jchick
Well they said negative right?
annie12m
  • annie12m
yeah
annie12m
  • annie12m
so lets try putting it p and q negative in all the operations
jchick
  • jchick
Actually wait.
jchick
  • jchick
Just compare the two statements if they match then select it.
annie12m
  • annie12m
what you mean?
jchick
  • jchick
c and d
annie12m
  • annie12m
it goes in this order.. A. p + q is a negative integer B. p • q is a positive integer C. p – q is a negative integer D. p/ q is a negative integer
jchick
  • jchick
Well A is positive. so that is false
annie12m
  • annie12m
you sure its not a and c?
annie12m
  • annie12m
a negative plus a negative equals a negative
annie12m
  • annie12m
Numbers p and q are negative integers.
jchick
  • jchick
Oops you are right I misread it. Sorry you are right the first one is negative.
annie12m
  • annie12m
ok
jchick
  • jchick
Because if p = -2 + q = -2 you get - four.
annie12m
  • annie12m
ya
jchick
  • jchick
Ok so how about multiplication?
annie12m
  • annie12m
so is it a and c?
jchick
  • jchick
Tell me the rule for multiplying two negatives.
annie12m
  • annie12m
multipulcation well a negative times a negative or a positive times a positve you get a positive and a negative time a positive or a positive times a negative you get a negative
annie12m
  • annie12m
oh so b would be it too
jchick
  • jchick
two negatives make a positive
jchick
  • jchick
In multiplication.
annie12m
  • annie12m
yeah
jchick
  • jchick
Ok I didn't understand what you had said.
jchick
  • jchick
So yes it would be B
annie12m
  • annie12m
i said the same thing you said but i said it for all of them
annie12m
  • annie12m
ok now we see subsraction
jchick
  • jchick
Wait
jchick
  • jchick
Subtracting a negative by a negative is a positive.
jchick
  • jchick
-2--2
jchick
  • jchick
This equals 0
annie12m
  • annie12m
-6 - (-3) you keep the first number then switch it to addition then change the sign of the last number so now it is -6 plus 3 and that equals -3
jchick
  • jchick
Yes correct
annie12m
  • annie12m
its still negative so its correct so c is also correct
annie12m
  • annie12m
now lets try division
jchick
  • jchick
-8/-4 = +2
annie12m
  • annie12m
thats wrong
jchick
  • jchick
If the 2 numbers you are multiplying or dividing have the SAME sign (+,+ or -,-) then the result is POSITIVE
annie12m
  • annie12m
so its a, b, and c
annie12m
  • annie12m
next question
jchick
  • jchick
Correct!
annie12m
  • annie12m
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}
annie12m
  • annie12m
do you know what rational numbers are?
jchick
  • jchick
Ok so if you add any two elements of a set and you ALWAYS get another element in the set, that set is closed under addition. For example 2+2=4 2+4=6 and 4 and 6 are part of the even number set.
annie12m
  • annie12m
so even would be correct
jchick
  • jchick
let's go through each set a) no 5 + 2 = 7. 7 is not in the set. b) yes c) yes d) 0+0=0
annie12m
  • annie12m
so b c and d?
annie12m
  • annie12m
but what are rational numbers?
jchick
  • jchick
B. even integers C. rational numbers D. {0}
jchick
  • jchick
a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, p and q, with the denominator, q, not equal to zero.
jchick
  • jchick
In easy terms A number that can be made by dividing two integers.
annie12m
  • annie12m
but what does that have to do with addition? so its not correct?
jchick
  • jchick
What I have posted is the correct answer.
jchick
  • jchick
Closure: The result of adding two rational numbers is another rational number.
annie12m
  • annie12m
ok ill do those 3 as the answer then
jchick
  • jchick
Ok
jchick
  • jchick
Any more questions?
annie12m
  • annie12m
now next question
jchick
  • jchick
Ok
annie12m
  • annie12m
oh just 2 more left
jchick
  • jchick
Ok shoot.
annie12m
  • annie12m
Which equations show that the set of whole numbers is not closed under subtraction? Choose all answers that are correct. A. 1 – (–2) = 3 B. 1 – 2 = –1 C. 2 – 0 = 2 D. 2 – 4 = –2
annie12m
  • annie12m
oh and stay close attention to where it says NOT
jchick
  • jchick
Cave, in order to show closure for a set, you need to start with two elements in the set. (Keep in mind that negative numbers are NOT in the set of Whole numbers). So you need to look for which one starts with two whole numbers, then ends up with something that is not a whole number
jchick
  • jchick
It's not A
annie12m
  • annie12m
b is correct?
jchick
  • jchick
option A shows us doing subtraction with a negative number. Negatives are not in the set of whole numbers. You need to start with this whole number - whole number =
annie12m
  • annie12m
ok
jchick
  • jchick
Yes B is correct
jchick
  • jchick
It's not C. C does not show us leaving the set of whole numbers. See how the result is still positive.
annie12m
  • annie12m
yea i see
jchick
  • jchick
D sounds correct, you start with two elements in the wholes, then doing subtraction, you left the set of whole numbers. And B also? Yay good job \c:/
annie12m
  • annie12m
so b and d got it
jchick
  • jchick
Ok so last question!
annie12m
  • annie12m
For which operations is the set {0, 1} closed? Choose all answers that are correct. A. multiplication B. division C. addition D. subtraction
jchick
  • jchick
If we do this: 0−1 Do we end up with a number which is in the set?
annie12m
  • annie12m
ya
jchick
  • jchick
Are you sure?
annie12m
  • annie12m
wait no
annie12m
  • annie12m
because it equals -1
jchick
  • jchick
Good so we can eliminate D right?
annie12m
  • annie12m
ya
jchick
  • jchick
1/0 How bout division? Do we end up with an element in the set if we do this?
annie12m
  • annie12m
0 +1 equal 1 and 1+0 equals 1 so addition works?
annie12m
  • annie12m
yep it equals 1
annie12m
  • annie12m
so addition and division works
jchick
  • jchick
So did you understand the last question cave? :O 1+1 We are not closed under addition
annie12m
  • annie12m
oh right forgot about that you can do the number more than once
jchick
  • jchick
So does the division work?
annie12m
  • annie12m
division works though
jchick
  • jchick
The whole numbers are closed under addition. There is no way to add two whole numbers to get a nonwhole number.
annie12m
  • annie12m
and multipulcation because 0 times 0 equals 0 and 1 times 1 equals 1 and 1 times 0 equals 0
jchick
  • jchick
Wait are you sure?
jchick
  • jchick
Try again.
annie12m
  • annie12m
yeah im sure its division and multipulcation, am i wrong?
jchick
  • jchick
No division by zero in the land of math. So division is also a no no.
annie12m
  • annie12m
ok so only multipulcation then?
jchick
  • jchick
Yes.
annie12m
  • annie12m
ok let me sumbit the quiz and see what i got
jchick
  • jchick
Ok
jchick
  • jchick
What did you get?
annie12m
  • annie12m
i failed the last one was multipulcation and division not just multipulcation, the one before the last one was correct, so was the one before the other one, the one before that one was incorrect it was only a and b not a b and c, and the first one was correct
jchick
  • jchick
Wait that doesn't make any sense.
jchick
  • jchick
Oh I see on the last one sorry.
annie12m
  • annie12m
so got 2 wrong :( i didnt put division in it and i added one when it was only suppose to be a and b not c
jchick
  • jchick
The one before was not wrong I don't understand. You should ask your teacher.
jchick
  • jchick
Wait I said not C
annie12m
  • annie12m
i will, well thanks anyways! well is there any way i can reward you for your time and help? you did help me understand a lot
jchick
  • jchick
Well you can select best response.
jchick
  • jchick
But I am sorry if I confused you I did say not C.
annie12m
  • annie12m
ok i did that and i clicked become a fan
jchick
  • jchick
Thank you so much!
annie12m
  • annie12m
well i gtg now, bye!
jchick
  • jchick
Bye!
jchick
  • jchick
@mathmale please look over my work and make sure because apparently I was wrong.

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