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Hey all,
I'm very sorry that this is off topic, but I couldnt find anywhere else to ask this type of question on the web.
Does anyone know of a GOOD message board for discrete structures/discrete math?
Anyways, I mine as well as the question.
A function g is defined as g(A) = T U (A /\ S) where T, S are fixed subsets of universe U . Does g have an inverse? If so, what is it. If not, why not?
( /\ is intersection operator )
Thank you all and sorry again for the off topic post!!
Justin
Link to FD's Math Forum
3 years ago, I could have done that problem for you, but I barely got out of that class and I sure don't remember much from it. I think that was one of the most confusing classes I ever took in college.
g(A) = T U (A /\ S)
This is invertible only if g(A) is one-to-one and unto.
I was thinking if we can prove the inverse may not exist by counter-example:
Let say
U = {1,2,3,4,5,6,7,8,9,10,11,12}
T = {1,2,3,4}
A = {5,6,7,8}
S = {9,10,11,12}
g(5) = {1,2,3,4} // since 5 /\ S is an empty set
= T
g(6) = {1,2,3,4} // for same reasons
= T
5!=6 but g(5) = g(6), therefore it may not be one to one.
Correct if i am wrong.