Compare the following compound statements. (pVq) ∧  ~q                ;             pV (~q ∧ ~p) Is there tautology? Is there a self-contradiction? Are the statements logically equivalent, negations, or neither?

The answer provided did not use the rules of inference to prove that the propositions are tautologies which is what the original question asked. Can the answer to this problem be provided by using the rules of inference?

Using relational predicates ( e.g. F(s,m) for, say, s can fool m), translate the following sentences into predicate logic. You can use English words for the quantification symbols (such as For All x instead of v x) if necessary Also give the negatives of each sentence in English. a) Everybody can fool somebody b) There is no-one who can fool everyone. For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac).

D part only plz. Thankyou.

Hello. Please answer the attached Discrete Mathematics question correctly and follow all directions. *If you answer correctly I will provide a thumbs up for you. Thank you.

• (Fill in the blanks) A tautology is a proposition which • A contradiction is a proposition which • The contrapositive of the conditional P Q is the conditional • True or False? The contrapositive of P = Qis logically equivalent to P = Q. • The converse of the conditional P Q is the conditional • The converse of P → Qis always logically equivalent to P » Q. • The negation of the conditional P = Q is the proposition • State de Morgan's laws for propositions P and Q: ¬(P V Q) ¬(PA Q) + Exercises 2.1.1 Express each of the following statements in the "If ..., then ..." form. There are many possible correct answers. (a) You must eat your dinner if you want to grow. (b) Being a multiple of 12 is a sufficient condition for a number to be even. (c) It is necessary for you to pass your exams in order for you to obtain a degree. (d) A triangle is equilateral only if all its sides have the same length.