Is the following sentence a proposition? If it is a proposition, determine whether it is true or false.   “In the year 2000, Montreal was the capital of Quebec.”

Which statement is NOT correct? O A. Every WFF is equivalent to a WFF in prenex normal form. B. Skolemization does not change the meaning of sentences. C. Skolemization generates equisatisfiable sentences. D. A formula in Skolem form does not have existentially quantified variables.

Construct a truth table to decide if the two statements are equivalent. ~p ∧ ~q; ~(p ∨ q) TRUE FALSE

Consider the following true propositions:• p : The applicant has passed the learner permit test.• q : The applicant has passed the road test.• r : The applicant is allowed a driver’s license.For each of the following sentences write,symbolically, the compound proposition that correspondstothe given sentence in English asit is written (do not change the order or form of the expression).a) The applicant did not pass the road test but passed the learner permit test.b) If the applicant passes the learner permit test and the road test, then the applicant is allowed adriver’s license.c) Passing the learner permit test and the road test are necessary for being allowed a driver’slicense.d) The applicant passed either the learner permit test or the road test, but not both.e) It is not true that the applicant does not pass the road test and is allowed a driver’s license.

Part A: Which of the following is a quantified statement? a. Go, Eagles! b. When will I be loved? c. Go, Cougars! d. Honey is sweeter than sugar. e.No dogs are cats. Part B: Which of the following is a quantified statement? a. Wild animals need to be protected. b. Your pudding is hard as a rock. c. My car is green. d. This sentence is false. e. Some movies are too long.

Part H For each argument, write a symbolization key and translate the argument as well as possible into SL. The part of the passage in italics is there to provide context for the argument, and doesn’t need to be symbolized.   3. A westerner tries to predict the policies of the Chinese government. If the Chinese government cannot solve the water shortages in Beijing, they will have to move the capital. They don’t want to move the capital. Therefore they must solve the water shortage. But the only way to solve the water shortage is to divert almost all the water from the Yangzi river northward. Therefore the Chinese government will go with the project to divert water from the south to the north.

Q: The propositional variables b, v, and s represent the propositions: b: Alice rode her bike today. v: Alice overslept today. s: It is sunny today. Select the logical expression that represents the statement: “Alice rode her bike today only if it was sunny today and she did not oversleep.”  b→(s→¬v)     2. b→(s∧¬v)   3. s∧(¬v→b) 4.  (s∧¬v)→b Group of answer choices b→(s∧¬v) b→(s→¬v) s∧(¬v→b) (s∧¬v)→b   2);  The following two statements are logically equivalent   (p → q) ∧ (r → q) and (p ∧ r) → q Group of answer choices True False