Question

Anybody in here completed Discrete Mathematics course yet?

Answer 1

Which field of Discrete Mathematics ?

Answer 2

Number Theory,Combinatorics,Set Theory ,Probablity,Operations Research,Game theory, decision theory, utility theory, social choice theory,Discretization,Hybrid discrete and continuous mathematics...........................There are many which one?

Answer 3

I am currently taking a Discrete Mathematics for Computing course, and was looking for some help with different problems from that course. We are currently working on propositional logic and I was having a little trouble with a couple of problems.

Answer 4

There is a discrete mathematics group, but there is practically no activity in it, so I thought I'd give this group a try to see if someone was available that might could help out.
Here's one of the problems that I can't figure out.
"Express these statements using logical operators, predicates, and quantifiers.
a) Some propositions are tautologies.
b)The negation of a contradiction is a tautology.
c)The disjunction of two contingencies can be a tautology.
d)The conjunction of two tautologies is a tautology.

The answer supposed that T(x) is a tautology and C(x) is a contradiction. The answer for A is\[\exists x T(x)\] just so you get the form they are looking for in the answers.
I got A without any problem, but I didn't get the answers provided in the back of the book for the other three problems.
b) I got \[\forall x ( \not C(x) \rightarrow T(x))\]the book said \[\forall x ( C(x) \rightarrow T( \not x)\]. I couldn't find the regular negation sign in the equation editor so the slash through the letter indicates negation. What does my answer not work?
For the other two, I did not get the given answers at all. What would you get for these?
Thanks for your help!

Answer 5

You should try the Mathematics group.

Answer 6

a) Some propositions are tautologies.
Tautologies being defined as a statement form that is always true regardless of truth values of the individual statements substituted for its statement variables.
Say you have this proposition:
p v ~p. Whatever boolean type you give "p" this will always logically be true.


b)The negation of a contradiction is a tautology.
This goes back to what a negation is, which is just the opposite of a given proposition. A contradiction is a proposition that will always come out false, such as "p and ~p"
If a contradiction is always false, the negation would have to be a statement that is always true, which is a tautology.

c)The disjunction of two contingencies can be a tautology.
Such as I stated in question A. If you have p OR not p. You truth values will always be true, or a tautology.

d)The conjunction of two tautologies is a tautology.
If you conjoin two tautologies with an "AND" operator. The truth value will always be true, which is obvious. True AND True is always True. Since a tautology is always true.

∀x(C(x)→T(/x), Think about what the book is saying.
"For all values 'x', The contradiction of x implies the negation of a tautology.

I'm not too sure if I truly (pun intended) answered any of your questions, but I hope I at least helped!