Math – infinite loop

Sometimes we need to show that a claim is false. This can be done by finding a counterexample. Consider any claim of the form: . To show that the claim is false, we need to find a value of $x\in S$ for which P_x is true and Q_x is false.

That is, we need to prove the negation of the above claim: $\exists x\in S\mid P_x\wedge \overline Q_{x}$ . Finding any that supports the negation of the original claim is sufficient to disprove it. Continue reading “Disproof by Counter Example”