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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:

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