Below are an attempt at deductions. In this case , suppose that we know that tha

Question

Below are an attempt at deductions. In this case , suppose that we know that that the first two propositions are true, and wish to deduce that the third is true.

In each of parts (i) state whether the deduction is valid. If it is valid, give a deduction combining proof by contradiction and Modus Ponens. If it is not valid, explain why not.

(i) We know that:

If an equation is quadratic, then Michelle can solve it.

Michelle cannot solve the equation f(x) = 0

We conclude that :

The equation f(x) = 0 is not quadratic.

Thanks for help !

Explanation / Answer

Hi..

1. If an equation is quadratic, then Michelle can solve it.

2. Michelle cannot solve the equation f(x)=0.

3. The equation f(x)=0 is not quadratic.

This is a valid inference using modus tollens. Given If P then Q, ~Q we can conclude ~P. Here P= an equation is quadratic, Q=Michelle can solve it. Thus ~Q is Michelle cannot solve the equation and ~P=the equation is not quadratic.

Modus ponens is If P then Q,P implies Q. In this case it would be If an equation is quadratic then Michelle can solve it, and the equation is quadratic which implies that Michelle can solve the equation.

For the given information, assume (1) and temporarily assume the negation of (3) (the equation is quadratic.) Then we have a contradiction since if the equation was quadratic, Michelle would be able to solve (using modus ponens) it but we are given (2) Michelle is unable to solve the equation. Thus the temporary assumption that the equation is quadratic must be false,so the equation is not quadratic.

Related Questions

Navigate

• Browse (All)
• Browse B
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.