Answer the following questions in the space provided below. 1. For each proposition below, first determine its truth value, t
Answer the following questions in the space provided below. 1. For each proposition below, first determine...
true and false propositions with quantifiers. 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 De Morgan's laws) to eliminate all – symbols. All variables are from the domain of integers. (a) 3.0, x2 <. (b) Vr, ((x2 = 0) + (0 = 0)). (c) 3. Vy (2 > 0) (y >0 <y)). 2. Consider the predicates defined below. Take the domain to...
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))
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...
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)...
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....
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...
Answer the questions in the space provided below. 1. The definition of a function f: X + Y is as a certain subset of the product X x Y. Let f: N + N be the function defined by the equation f(n) = n2. For each pair (x, y) listed below, determine whether or not (x,y) ef. a) (2,4) b) (5, 23) c) (1,1) d) (-3,9) 2. For each function defined below, state whether it is injective (one-to-one) and whether...
Please answer the problems after f and please explain the reasoning (1) For each assertion below, indicate if it is true (T) or false (F) by circling the correct response. (a) (T, F) The statement, "this statement is false” is a proposition. (b) (T, F) The statement "If I am Spider-Man, then I can breath in space" is true. (c) (TF) The statement "Spider-Man can breath in space" is true. (d) (T. F) "F →p can be false. (e) (T,F)...