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The following propositional statement is  $\left(P \implies \left(Q \vee R\right)\right) \implies \left(\left(P \wedge Q \right)\implies R\right)$

  1.    satisfiable but not valid
  2.    valid
  3.    a contradiction
  4.    None of the above
in Mathematical Logic by Veteran (52.2k points)
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1 Answer

+23 votes
Best answer
Answer a

It is false when P = T, Q = T, R = F

It is true (satisfiable) when P = T. Q = T, R = T
by Loyal (5.7k points)
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what does it means '' not valid '' in option a ?????

Tautology: A tautology is a proposition that is always ture. 

ex: (p  v ~p)= T

Contradiction: A contradiction is a proposition that is always false.

ex: (p ^ ~p)=F

Contigency: A contigency is a proposition that is neither a tautology nor a contradiction.

ex: (p v q)----> ~r

* A propositional logic is said to be satisfiable if it is either a tautology or contigency.

* If logic is contradiction then it is said to be unsatisfiable.

* By contigency we means the logic can be ture or false.

* Contradiction is the unsatisfiable function.

* Statement is valid means tautology.

* Statement is not valid means not tautology.

You can reduce the equation to $P' + Q' + R$ by using $A \rightarrow B \equiv A' + B$

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