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

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