Explain in this definition ”The proposition P → Q is FALSE if P is TRUE and Q is FALSE; otherwise, P → Q is TRUE” why If False then False or If False then Trueevaluates as True? You can give an example.

Create a truth table for (p V q)Ar.

Q4. How many rows are in a truth table for a compound proposition with 2 propositional variables (for example, p, q, r ...)? Your Answer: Answer

2. Is the definition of a tautology an existential statement or a universal statement? Can you depend on luck to show that a proposition is a tautology? Explain your answer.

2. (P + Q)=(Q→P) Build the truth table. P P +Q Q +P According to the truth table you built, are these statements logically equivalent? Why or why not?

RMM2.1 -3

Using rules of inference, laws of logical equivalences, and other definitionstaught in class, show that the premises conclude with “It is not true that“If I turn in my homework, then I will go to sleep early”” Be sure todefine all propositional variables for full credit. Remember, it is possiblethat you will use all premises, but it is also possible that some are notneeded. a.) Today is Friday and Papa Johns is on fire.b.) I will win a chess match if today is a Friday or I do not watch amovie.c.) I sleep early only if I do not win a chess match.d.) I will get to class on time and turn in my homework if I do not sleepearly.e.) Papa Johns is not on fire if and only if I do not turn in my homework.f.) Domino’s is not on fire today.

Please provide an answer for this question

Contrast a truth table for the statement  pV~p

Help please