First this is my first attempt at using latex to ask a question, so my appologies if the statements come out strange. I'll edit as needed.
Homework Statement
Let R and S be relations on a set A. Prove that if R \subseteq S, then R^{n} \subseteq S^{n} for all n \geq 1
Homework Equations...
Homework Statement
Let R1 and R2 be the "congruent modulo 3" and "congruent modulo 4" relations on the set of integers.
Homework Equations
Find:
a) R1 \cupR2
b)R1 \cap R2
There is also problem c, d but I won't write these here. If I am able to solve this, then the rest should be...
Alright well I just figured it out.. i really need to stop pulling these all nighters and my only source of nutrition being candy bars and coffee.
The answer is so obvious and I definitely didn't see it.
Homework Statement
For each of the following relations on the set of all real numbers, say whether it is reflexive, symmetricm anti-symmetric, and transitive.
Homework Equations
c)x=1
The Attempt at a Solution
According to class notes I took, as this simple question was solved in class...
Thanks for your input statdad, anything is appreciated! Knowing my teacher, she would look into specifics as well and that's why I had to ask.
I was thinking of proving that statement with another case by induction
( I gave up trying to use latex code, it's really messing up on me and not...
Hey guys, this is a problem given to us by our professor in one of the worksheets. I would like an opinion to see if this proof is valid
Homework Statement
Use mathematical induction to prove that 3^{n}+7^{n}-2 is divisible by 8 for \foralln\inZ^{+}Homework Equations
Base step:
n=0...