true and false propositions with quantifiers. Answer the following questions in the space provided below. 1....
Answer the following questions in the space provided below. 1. For each proposition below, first determine its truth value, then negate the proposition and simplify (using DeMorgan's laws) to eliminate all – symbols. All variables are from the domain of integers. (a) 3x, 22 <2. (b) Vx, ((:22 = 0) + (x = 0)). (e) 3xWy((x > 0) (y > 0 + x Sy)). 2. Consider the predicates defined below. Take the domain to be the positive integers. P(x): x...
1 15 oints) Deterine if the following propositions are TRUE or FALSE. Note that p, q r are propositi Px) and P(x.y) are predicates. RUE or FALSE.Note that p, q, r are propositions. (a).TNE 1f2小5or I + 1-3, then 10+2-3or 2 + 2-4. (b).TRvE+1 0 if and only if 2+ 2 5. (d). _ p v T Ξ T, where p is a proposition and T is tautology. V x Px) is equivalent to Vx - Px) (g). ㅡㅡㅡ, y...
9. Prove that the following kogical expressions aro logically equivalent by applying the law of logic 10. Give a logical expression with variables p, q, and r that's true only if p and q are false and r is true. 11. Predicates P and Q are defined below. The domain of discourse is the set of all positive integers. P(x): x is prime Qlx): x is a perfect square Are the following logical expressions propositions? If the answer is yes,...
Predicates P and Q are defined below. The domain of discourse is the set of all positive integers. P(x): x is prime Q(x): x is a perfect square (i.e., x = y2, for some integer y) Find whether each logical expression is a proposition. If the expression is a proposition, then determine its truth value. 1) ∃x Q(x) 2) ∀x Q(x) ∧ ¬P(x) 3) ∀x Q(x) ∨ P(3)
Predicates P and Q are defined below. The domain of discourse is the set of all positive integers. P(x): x is prime Q(x): x is a perfect square (i.e., x = y2, for some integer y) Indicate whether each logical expression is a proposition. If the expression is a proposition, then give its truth value. (c) ∀x Q(x) ∨ P(3) (d) ∃x (Q(x) ∧ P(x)) (e) ∀x (¬Q(x) ∨ P(x))
Let the predicates P,T, and E be defined below. The domain is the set of all positive integers. P(x): x is odd T(x, y): 2x < y E(x, y, z): xy - z Indicate whether each logical expression is a proposition. If the expression is a proposition, then give its true value and show your work. If the expression is not a proposition, explain why no. 1(a) P(5) 1(b) ¬P(x) 1(c) T(5, 32) 1(d) ¬P(3) V ¬T(5, 32) 1(e) T(5,10)...
Attempt 1 Question 1 (1 point) Consider the following simple propositions. p: The student does well on the final. q: The student studies. w Translate the following compound proposition using logical connectives, and the simple propositions, p and q: "There are some students in the class who do well on the final whenever they study." (You may copy and past the following symbols as needed V.3 v. ,-)
Please answer question 1 and 2. (1) Let p, q be propositions. Construct the truth table for the following proposition: (2) Let X be the set of all students in QC and let Y be the set of all classes in the Math Department available for QC students in the Fall 2019. Leyt P(z, y) be the proposition of the course y. Write down the following propositions using quantifiers: e Some QC students read the description of each course in...
16 pts) #4. TRUE/FALSE. Determine the truth value of each sentence (no explanation required). ________(a) A statement is a sentence that is true. ________(b) In logic, p q refers to the "inclusive or, " true when either p or q or both are true. ________(c) The phrase "not p and not q" means "not both p and q." ________(d) The conditional statement p q is true if p is false. ________(e) The negation of p q is p ~q. #5....
Simplify the following sentences in predicate logic so that all the negation symbols are directly in front of a predicate. (For example, Vx ((-0(x)) + (-E(x))) is simplified, because the negation symbols are direct in front of the predicates O and E. However, Væ -(P(2) V E(x)) is not simplified.) (i) -(3x (P(x) 1 (E(x) + S(x)))) (ii) -(Vx (E(x) V (P(x) +-(Sy G(x, y))))) Write a sentence in predicate logic (using the same predicates as above) which is true...