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Constractive dilemma

solakis

Active member
Dec 9, 2012
304
Right any high school algebra proof where the constractive dilemma propositional law is used


Constractive dilemma being the following propositional law:

From PvQ and P=>S and Q=>T we can infer SvT
 

solakis

Active member
Dec 9, 2012
304
Right any high school algebra proof where the constractive dilemma propositional law is used


Constractive dilemma being the following propositional law:

From PvQ and P=>S and Q=>T we can infer SvT


An example:

Prove:\(\displaystyle \forall x(x^2\geq 0)\)

Proof:
\(\displaystyle x\geq 0\vee x<o\)

1) for \(\displaystyle x\geq 0\implies x.x\geq 0.x\implies x^2\geq 0\)

2) for \(\displaystyle x<0\implies (-x)>0\implies (-x)(-x)>0\implies x^2\geq 0\)

Now if we put P=\(\displaystyle x\geq 0, \)Q=\(\displaystyle x<0\)

AND S=T=\(\displaystyle x^2\geq 0\)

We have the application of the constractive dilemma propositional law in the above proof