Let the universe consists of all people. Consider the following hypotheses: • Some students like all teachers. • No student likes any dishonest person. Using first-order logic prove that "no teacher is dishonest". Use the following predicates for your proof: S(x) denotes x is a student; T(x) denotes x is a teacher; D(x) denotes x is dishonest; L(x,y) denotes x likes y.

I need help in this Discrete Mathemathics Question based on the Consistent System Specs. This is the statement- The student either has undergraduate courses or post-graduate courses, but not both. The student does not have undergraduate courses unless he does not have a bachelor’s degree. The student has a bachelor’s degree only if he has post-graduate courses. The student has undergraduate courses. I need help in determining whether the given specification is consistent or not using Rules of Logical Equivalences.

Using truth tables, or in any other way, prove that each of the following compound propositions is not a tautology. These implications are common logical fallacies (errors in reasoning) since the conclusion does not follow logically from the set of hypotheses. a. [(P⇒ Q) ^ Q] ⇒ P. b. [(PQ) ^ (~ P)] ⇒ (~ Q). For each one of the logical fallacies in part (iii) of this question give an example of a "real life" situation where such an error can occur.

Which of the following can be turned into a proof of the following argument: -(PAQ), P..¬Q. (i) (ii) (iii) ¬(P A Q) 1 |¬(P^Q) 1 1 2 P P n+1 ¬(PAQ) (ii) (ii) O (i) 2.