Formal Proof of Hypotheses ?

Question

Hi

I have a maths exams coming up, and have a past exam paper which has questions that will be in the exam. There are a total of 2 questions, I want to know the answer and a description on how to do it. Thanks

Consider the following set of hypotheses about a cat called Felix:

If Felix does not get regular attention, he is not happy. If Felix is not happy, he scratches furniture. If Felix scratches furniture, his owner is angry. Felix’s owner is not angry.

a) Using the atomic sentences, express the hypotheses in symbolic form:

E : Felix gets regular attention

C :Felix is happy

F : Felix scratches furniture

A :Felix’s owner is angry

b) Construct a formal proof that the conclusion Felix gets regular attention follows from the given hypotheses.

Answer 1

Remember that the sign => means "implies" or "if...then"

The first statement becomes ~E => ~C {IF Felix does NOT get regular attention THEN Felix is NOT happy}

The second statement becomes ~C => F {IF Felix is NOT happy THEN Felix scratches the furniture}

The third statement becomes F => A {IF Felix scratches the furniture THEN Felix's owner is angry}

Put together this is:

~E => ~C => F => A or IF Felix does not get regular attention THEN Felix's owner is angry.

BUT when Felix's owner is NOT angry so we can read the logic in reverse.  That is, write it backwards, reverse the signs and change to the negative statements -

~A => ~F => C => E or IF Felix's owner is NOT angry THEN Felix gets regular attention