MHB Solving a High School Algebra Proof Using Constractive Dilemma

[solakis1]

Right any high school algebra proof where the constractive dilemma propositional law is usedConstractive dilemma being the following propositional law:

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

 

[solakis1]

Right any high school algebra proof where the constractive dilemma propositional law is usedConstractive dilemma being the following propositional law:

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

An example:

Spoiler

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

Proof:
$$x\geq 0\vee x<o$$

1) for $$x\geq 0\implies x.x\geq 0.x\implies x^2\geq 0$$

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

Now if we put P=$$x\geq 0, $$Q=$$x<0$$

AND S=T=$$x^2\geq 0$$

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