Yet another attempt:
I guess you have to start with the statement you want to prove first and use the given as you said.
So based on that:
if x in (A-C) then x is in A and x is not in C
then x in A
if x was not in B which just the compliment of B we can say that it also can be in the set...
Learned of the diagrams but it didnt seem to help me much. Unfortunately its been about 15 years (i just recently went back to school to pursue a new degree) and this is just an introductory course of mathematical proofs.
I guess what I fail to see is the actual relationship between these...
Yes that's correct.
thats the issue I'm having, I don't know how to proceed from here. It really doesn't make sense to me. Unfortunately the only things we went through in class was one step equavilence examples such as proof of de'morgan's law.
This is totaly different and new to me and...
I've been working on these problems and unfortunately i can't make heads or tails of these two.
Any insight where to start the proof would be great.
1)Let A, B and C be sets. Show that if A~B⊆C, then A~C⊆B holds.
What I got so far:
Is it correct to state that A~B = A⋂B' and A~C = A⋂C'...
Ah I see now. I think I got it now. Its definitely a lot easier then i set it out to be. Didnt notice the IF-THEN and givens. Many thanks for all the help its been greatly appreciated.
Thanks for the help, but unfortunately my teacher didnt really go through this very well nor touched on limit sequences.
"Therefore |g(x)-0|<ϵ_0= |g(x) |<ϵ_0. Thus δ_0= ϵ_0."
my thoughts on this was that since g(x) is actually bigger then f(x) we must take the condition to do the limit proof...
Homework Statement
Let f and g be functions such that 0≤f(x)≤g(x) for every x near c, except possibility at c. Use the definition of a limit to prove that if lim(x→c)g(x)=0 then lim (x→c)f(x)=0.
This is my attempt at this proof and I'm very poor at it. Can someone check and give me...