Need help for proof?

Question

Let A = {(x,y):0 B = {(x,y):0 Suppose (x,y) is in (A intercepts B). How do i prove x =y and 0

Answer 1

Start out by letting (x,y) be a point in AnB. As it is in AnB, it must be in A. So, x=>0 and y=>x. [We've gotten the x=>0 part, now we just need the x=y bit.] (x,y) is also in B, so x=>y. Now we have that y=>x and x=>y. The only way that is possible is for x=y.

QED

Answer 2

if (x,y) is in the intersection then
x<= y and y<= x then x=y (trichotomy law for real numbers)

if x is in A then x <=0.

You're done, right?

Just for kicks: plot the line y=x. Set A is on and above that line, Set B is on and below that line. The intersection is the line.

Answer 3

Find out how to add more letters of the alphabet to it ,,,,,