Question

Set Theory

Answer 1

Give me a sec I cant figure out how to write it out on here

Answer 2

Prove or disprove :
A is subset of B
B is a subset of A
B=C

Answer 3

To see if A is a subset of B, you need to show that if you take an arbitrary element in A, it must also be in B. However, for your first question, you'll have better luck trying to find a counterexample. My personal favorite is \(a=0\) so that \(x=2\). 2 is not in B because \(2+3=5\) and 5 is not a multiple of 10.

Thus, A is not a subset of B.

Answer 4

Now, is B a subset of A? Let's take a number \(y\in B\) and \(y=10b-3\). Now, notice the following. \[10b-3=5(2b)-3=5(2b-1)+2\]This means that \(y\in A\) with \(y=5(2b-1)+2\)

Answer 5

Now for the last one. Let's start with \(y=10b-3\) again. This means that \[10b-3=10(b-1)+7\]Since this is an equality, it implies that \(B\subseteq C\) and \(C\subseteq B\). Hence, \(B=C\).

Answer 6

okkk i seeee but i am confused as to th elogic behind what u did for the first 2

Answer 7

For the first one, I provided a counterexample. \(x=2\) is in A, but it isn't in B. This means that A isn't a subset of B since there is some element contained in A, but not B.

For the second one, I took an element in B. By definition it could be written as \(y=10b-3\). If you rearrange that, you can get a number of the form \(5a+2\) where \(a=2b-1\). Since A is defined as numbers of that form, any element in B must also be in A. Hence, \(B\subseteq A\).

Answer 8

Note that A={...,-13, -8, -3, 2, 7, 12, 17, ...} and B={..., -23, -13, -3, 7, 17, 27, ...}.
We can see that A is not a subset of B because some elements of A are not in B.
We can show this by noting that 2 belongs to A, but, because 2=10b-3 does not have an integer solution, 2 does not belong to B.

Answer 9

THANK YOU GUYYYSSSS :DDDDDDDDD

Answer 10

You're welcome.