Predicate logic - true or false formulae

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Predicate logic - true or false formulae

Hello everyone, I can't seem to understand how to do this question.

Determine whether the formula F:
(i) both P(a) and P(b) are true;

(ii) both P(a) and P(b) are false;

(iii) P(a) is true and P(b) is false.

Before I post my solution, please let me know if you think I'm not understanding the question. I think we are asked to write out all the interpretations for the 3 different cases and determine whether they make the formula true or false. If there are no false cases then the formula is true under the given interpretations - otherwise false. Here is my solution:

i) we can immediately see two cases which would make the formula false so it is false under interpretation i) :

ii) No need to check here because the premises would be false so the formula is true in every case.

iii) there are four cases, one of which is false so F is false under interpretation iii) :

So my final answers would be i) false ii) true iii) false

My answers for i) and ii) are matching with the answers sheet but our lecturer has provided me with the following solution for iii):

Can somebody please explain to me where I am wrong?
sparta123

Posts: 1
Joined: Sat Dec 28, 2013 1:35 pm

sparta123 wrote:Determine whether the formula F:
(i) both P(a) and P(b) are true;
(ii) both P(a) and P(b) are false;
(iii) P(a) is true and P(b) is false.

Is something missing here?

The question asks "Determine whether the formula F..." what? "Determine whether F" is true? Is false? Is sometimes true and sometimes false? How do "a" and "b" relate? Where did they come from? Your discussion refers to "interpretations". What does this mean?

stapel_eliz

Posts: 1797
Joined: Mon Dec 08, 2008 4:22 pm