Random_Doubt

Question

if it is given -> "Every satisfiable propositional formula is not tautology"

then what will it corresponds to?

i am writing its hindi, which among below two are correct?

1. "har ek satisfiable formula tautology nahi hota hai"  // it is indeed truth.

2. "koi bhi satisfiable formula hua, to wo tautology nahii hoga"  // this is false.

Comments

Satisfiable means the formula is true for at least one case.

And tautology means it is always true for all cases.

If this is true then we can say that satisfiability is a superset of tautology.

I agree with the comments you have written beside each statement.

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 Every (satisfiable propositional formula -> not tautology). = Every (Tautology  -> Not satisfiable propositional formula)= sare satisfiable proposition tautolgy nahi hote.

Satisfiable superset of Tautology.

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Wait what?? you wrote in very funny way in Hindi :p

Anyways Every satisfiiable is not tautology

But all tautology are satisfiable

Yahi ek conclusion hai....

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https://gateoverflow.in/7855/maths_mocktest1_11

Answer 1

I think whatever have you written is wrong i.e "Every satisfiable propositional formula is not tautology"

we know that a proposition is satisfiable if there is at least one true result in its truth table. if all are true then it is also satisfiable  and hence it is also tautology.