Use a truth table to determine whether the following is a valid argument: P⇒ (QR) Q→ (PR) (PVQ) ⇒ R. .. State the answer and explain why.

Consider the statement: If S = Ø then P(S) = Ø. (a) Is the statement true or false? (b) State the contrapositive. Is it true or false? (c) State the converse. Is it true or false? (d) State the contrapositive of the converse. Is it true or false? (e) Consider the statement: If S = Ø then P(S) ‡ Ø. Is this statement true or false? Is this statement equivalent to any of the statements above?

discrete math

Let P be the statement “You get perfect scores in your major exams,” Q be the statement “You do every exercise in your reference textbook,” and R be the statement “You obtained a grade of 1.00 in SEd Math223.”  a. Translate the statement ¬R⇒¬(Q∧P) in acceptable English.

Choose the appropriate proposition to be inserted in the shaded section to make a valid argument.  a. P→Q b. R→S c. ⅂(P→Q)→⅂ (R→S) d. (P→Q)→ (R→S)

Consider the following propositions: p="lt is cloudy" q="lt is rainy" F"l will play outside" s="l will stay at home" Select the inverse (s) of the follwing sentence: "I will stay at home and I will not play outside unless it is neither cloudy nor rainy" O None of all the proposed answers svr--pv -g SA r→pvq JA SL bL V d O

Consider the following argument: If the white flag is flying, then truce has been declared. Truce has not been declared. Therefore, the white flag is not flying. (a) Define statement variables for each component of the above argument, then write the formal argument using your variables. (b) Is the above argument valid? Explain. c) Find the contrapositive of the statement, “If the white flag is flying, then truce has been declared.” d) If the statement “If the white flag is flying, then truce has been declared” is replaced with its contrapositive, will the above argument be valid? Why or why not?

Question 2: LO2 - Logic 2.1. Consider the argument form: Premise 1: x V y Premise 2: xA¬y→z Premise3: y → x Therefore, z

Suppose ¬[(p → q) → (q → p)] is false. Can p→q have both possible truth values? Explain.

4. Consider the following differential equation in one dimension x² y" – 8xy' + 18 y = 0, a) Solve for y (x) using power series methods. b) If y (1) = 1, and y' (1) = 0, what is y (-1) = ? %3D