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1 votes
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22) S1: A formula is valid iff its complement is not satisfiable

     S2: A formula is satisfiable iff its complement is not valid.

Which statement is/are true?

 

a) Only S1 b) Only S2 c) both S1 and S2 d) none

2 Answers

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1 votes

S1: A formula is valid iff its complement is not satisfiable

Here, it says a formula is valid(Tautology) iff complement is not satisfiable means unsatisfiable i.e. Contradiction.

So, S1 is true.

S2: A formula is satisfiable iff its complement is not valid

It means, a formula is satisfiable(Tautology or Contingency) iff its complement is not valid or invalid(Contradiction or contingency).

That's also true

So, answer is (c) both S1 and S2.

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i think 3 is correct answer.

1. if S is  set of formula tha S' is the set of not valid formula area .

2. if we pick the element from S than it's complement  belong to S'.

if i am wrong than correct me.

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