Register

[Discrete Maths] predicate logic

1,203 views
1 1 vote

Whether following statement is correct?

Every satisfiable is not tautology.

I am reading it as:-

1st way :- If it is satisfiable then it is not tautology. So it should be false

2nd way:- It is same as saying that every satisfiable is not tautology because there are some satisfiable which are not tautologies as they are contingencies.

Please clarify which is correct and why?

2 Answers

5 5 votes
Case 1: If for all the assignment to proposition variable if you get TRUE always then it is SATISFIABLE as well as TAUTOLOGY.

Case 2: If for any assignment to proposition variable if you get TRUE then it is SATISFIABLE but not TAUTOLOGY.

So statement "EVERY SATISFIABLE IS NOT TAUTOLOGY" True
1 1 vote
>tautology means if there all true results in its truth table

>contradiction means if there all false results in its truth table

>contingencies proposition that is neither tautology nor contradiction(at least one value is true and atleast one false value)
a proposition is satisfiable if there is at least one true result in its truth table. so if any preposition is satisfy tautology or contigency then it is satisfiable,
Voting & Accepting an answer helps improve the community
← Previous · CountingNext → · time and work
← Previous in category · CountingNext in category → · [Discrete Maths] pre...
Position:
Show:

Related questions

3 3 votes
1 1 answer
761
761 views
rahul sharma 5 asked Jan 24, 2018
761 views
[Discrete maths] Predicate logic
Which of the following is true about below predicate logic P?A) P is satisfiableB) P is tautologyC) P is contradictionD) NoneThis expression in the end reduces to:-~ ∀z {...
2 2 votes
2 2 answers
2.5k
2.5k views
rahul sharma 5 asked Nov 16, 2017
2,510 views
Discrete maths:- Predicate logic
Consider $F(P), Q(P), L(P)$ denotes statements “Printer $P$ is out of service”, “Print job $P$ is queued” and “Print job $P$ is lost” respectively. Then statement “If a j...
1 1 vote
2 answers 2 answers
1.4k
1.4k views
rahul sharma 5 asked Jul 28, 2017
1,449 views
Discrete maths Predicate logic
( ∃x(P(x))→∃x(Q(x)) ) → ( ∃x(P(x)→Q(x)) )( ∃x(P(x)→Q(x)) ) → ( ∃x(P(x))→∃x(Q(x)) )Which of the above is valid and for not valid please give me counter example where LHS i...
0 0 votes
1 1 answer
1.7k
1.7k views
rahul sharma 5 asked Jun 18, 2017
1,719 views
[Discrete Maths] predicate Logic
Represent using logic connectives :- 1. "Whenever there is an active alert, all queued messages are transmitted."Given answer is :-∃x(Alert(x)∧Active(x))→∀y((Message(y)∧Q...