Answer the following questions with a yes or no. A) If it is true that x>y and it is also true that x < z, does that mean y < z is true?B) If it is true that x >= y and it is also true that z == x, does that mean that z == y is true?C) If it is true that x != y and it is also true that x != z, does that mean that z != y is true?
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Answer the following questions with a yes or no.
A) If it is true that x>y and it is also true that x < z, does that mean y < z is true?
B) If it is true that x >= y and it is also true that z == x, does that mean that z == y is true?
C) If it is true that x != y and it is also true that x != z, does that mean that z != y is true?
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- 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 ~qThe next two questions refer to the following belief network with random variablesF0,F1,…,F4 which only take the values 0 and 1. Which of the following statements are true about this belief network (1), (3) and (4) only :(1) F0 and F3 are independent given F1,F2 ;(2) F0 and F2 are independent;(3) P(F0∣F1,F2)=P(F0∣F1,F2,F3,F4) ;(4) F0 and F4 are independent. In general, to define the joint probability distribution P(F0,…,F4) one requires up to 25−1 entries in the table of probabilities. For the belief network above, one can compute the joint probability distribution P(F0,…,F4) using the following number of conditional probabilitiesAnswer the following sentence with "True" or "False":
- Determine 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) -> ¬pDetermine the truth value of the propositional form below given that p is false, q is true, and r is true. (Identify if it is True or False): r∨(p∧∼q)Which of the following statements about supervised learning is false?
- 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 iiiDetermine whether the following statements are logically equivalent or not. Show your work to clearly indicate your answer. p→¬qand¬(p→q)1a.Suppose P is a false statement. Is it ever possible for P ⇒ Q to be false? Explain your answer. 1B.Suppose P is a true statement and that (P ∧ Q) ∨ ¬P is false. What is the “truth value” of Q? (No work needbe included with this question). 1C.Write down a non-statement, and explain why it is not a statement.
- The statement "Every yellow dog has fleas" together with the statement "Fido is a blue dog". Which of the following is TRUE about the given premises. a.)modus tollens b.)modus ponens c.)modus ponens does not apply d.)modus tollens does not applyWrite the following two statements in symbolic form and determine whether they are logically equivalent. Include a truth table and a few words explaining how the truth table supports your answer. If Sam is out of Schlitz, then Sam is out of beer. Sam is not out of beer or Sam is not out of Schlitz.Determine whether or not the following statement is a tautology or not and give reasoning. If you need to, you can build a truth table to answer this question. (q→p)∨(∼q→∼p) A. This is a tautology because it is always true for all truth values of p and q. B. This is not a tautology because it is always false for all truth values of p and q. C. This is a tautology because it is not always false for all values of p and q. D. This is not a tautology becasue it is not always true for all truth values of p and q.