heh, guess I posted in the wrong grade level. Sorry, I'm new
Man I've become desperate, can anyone help me with these two problems?
Let A be the set {1,2,3,4}. Prove that a relation R on A with 15 ordered pairs is not transitive.
I've got no clue on that one.
And this second one, which I know the proof, but I need some help wording it correctly:
If f is injective (one-to-one) and C subset D are any subsets of A, then f(D-C) = f(D) - f(C).
Yeah that's similar to what I figured out. Here is my answer:
A relation R on A has 16 possible ordered pairs. Let R be a relation on A with 15 ordered pairs excluding aRc. Since all the other remaining pairs are in R, then aRb and bRc. However, since a does not relate to c, R is not transitive.
I just wasn't sure if that was enough.
may be the next proof appear to be silly but it is a try.
C is subset of D then D=(D-C)union C
f(D)=f(D-C)union f(C) (since the two sets are not intersecting) and given the function is one-to-one then we can say that f(D-C) and f(C) are also non intersecting which means that they are complimenting eachother with respect to f(D)
then f(D)-f(C)=f(D-C)