anonymous
  • anonymous
Anybody in here completed Discrete Mathematics course yet?
Calculus1
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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anonymous
  • anonymous
Which field of Discrete Mathematics ?
anonymous
  • anonymous
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?
anonymous
  • anonymous
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.

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anonymous
  • anonymous
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!
anonymous
  • anonymous
You should try the Mathematics group.
anonymous
  • anonymous
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!

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