Determine the truth value of the statement given that p is true, q is false, and r is false. 1. (p∧q)↔(p∨r) 2. (p∧∼q)∧(∼r∨q)
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Determine the truth value of the statement given that p is true, q is false, and r is false.
1. (p∧q)↔(p∨r)
2. (p∧∼q)∧(∼r∨q)
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- i need answer of all. if any answer will be skipped, your answer will be rejected. only complete answer will be accepted. b) Make a truth table for the statement ¬P ∧ (Q → P). What can youconclude about P and Q if you know the statement is true? a) Make a truth table for the statement (P ∨ Q) → (P ∧ Q). c) Make a truth table for the statement ¬P → (Q ∧ R).Construct a truth table for (p ∨ ¬ q) ∨ (¬ p ∧ q) Use the truth table that you constructed in part 1 to determine the truth value of (p ∨¬q) ∨ (¬ p ∧ q), given that p is true and q is false. Determine whether the given statement is a tautology, contradiction, or contingency. p V (~p V q) ~ (p ∧ q) ~p V ~qDetermine whether the following is true or false. Please cite the brief explanation so that I can know why is it true or false. A) 1 ∈ {{1},{2},{3}} B) A\B = A ∩ B^c C) The contrapositive of p -> (p V ¬p) = (¬p∧ q) -> ¬p
- 5. Suppose X and Y are both TRUE, A and B are both FALSE, P and Q are unknown, which of the following can have the identifiable truth value? a. (P ∨ X) → B s. ( X ∧ Y) → P d. (P→X) ∧ Q f. (A ∨ P) ⇔ XAnswer the following sentence with "True" or "False":use propositional logic to prove that the argument is valid. do not use truth tables ((¬A∨¬B)→(C∧D))∧¬D ∴ B
- Determine whether the following statements are logically equivalent or not. Show your work to clearly indicate your answer. p→¬qand¬(p→q)compute the truth value of the proposition ((¬q∧p) →r)<->(¬r→¬q)V P by completing the following truth table. the accepted response in each box is t or f.Determine which pairs of statements are equivalent.Note: You should be able to do this without a truth table.i. If I am happy, then the Giants won.ii. If the Giants win, then I am happy.iii. If the Giants lose, then I am unhappy.iv. If I am unhappy, then the Giants lose.Select all that apply:A. ii and ivB. i and ivC. iii and ivD. i and iiE. ii and iiiF. i and iii
- (1) Complete the truth table and determine whether or not ∼(p∨q)≡∼p∧∼q p q p∨q ∼(p∨q) ∼p ∼q ∼p∧∼q T T T F F T F F (2) Are the two statement equivalent? A. Yes, the columns are identical. B. No, the rows are not identical. C. No, the columns are not identical. D. Yes, the rows are identical.Construct a truth table to determine the truth value of the compound proposition (A ∧ B) ∨ (¬C ∧ D) where A, B, C, and D are propositional variables.38. If p is true, q is false, r is true, and s is false, what are the truth values of ~(q ⇔ s) and ~r ⇔ ~q, respectively?