Solved: Determine if each statement is a proposition. If so, also determine its truth value. Read and follow instructions. Ok I answered the assignment. 2+3=5 Let x be 5, x+y=10. DLSU-CCS is in Quezon City.

Let 𝐴={1,2,3,4}. Determine the truth value of each statement: i. ∀𝑥 ∈𝐴,𝑥+3<6 ii. ∃𝑥,𝑥+3<6 iii. ∃𝑥,2𝑥2 +𝑥 =15

Let Q(x)Q(x) be the statement “x + 1 > 2xx+1>2x ”. If the domain consists of all integers, let us find the following truth values. a) Since 1>0,1>0, we get that 𝑄(0)Q(0) is true. b) Taking into account that it is not true that 0…

Let Q(x) be the statement “x + 1 > 2x.” If the domain consists of all integers, what are these truth values? (7 pts.) a) 𝑄(0) b) 𝑄(−1) c) 𝑄(1) d) ∃𝑥𝑄(𝑥) e) ∀𝑥𝑄(𝑥) f) ∃𝑥¬𝑄(𝑥) g) ∀𝑥¬𝑄(𝑥)

20. Determine the truth value of each statement if the domain consists of all real numbers. (4 pts.) a) ∃𝑥(𝑥3 = −1) b) ∃𝑥(𝑥4 < 𝑥2) c) ∀𝑥((−𝑥)2 = 𝑥2) d) ∀𝑥(2𝑥 > 𝑥)

prove that n.P(n-1,n-1)=p(n,n)

Let R = {(1,4), (2,1), (2,5),(2,4),(4,3),(5,3),(3,2)} on the set A = {1, 2, 3, 4, 5}. Use Warshall’s algorithm to find transitive closure of R.

show that C(n+1,k)=C(n,k-1)+C(n,k)

Let f be the function from x ={0, 1, 2, 3, 4, 5} to X defined by f(x) = 4x mod 6. Write f as a set of ordered pairs and draw the arrow diagram of f . Is f one-to-one? Is f onto?

Which of the following functions are injective? Which are surjective? a) f: Z → Z given by f(x) = x2 + 1. b) g: N → N given by g(x) = 2x. c) h: R → R given by h(x) = 5x - 1.

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Create a schematic diagram of all odd numbers from 20 to 45

(a) If x is nonnegative, then x is positive or x is 0.

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1.b is defined by bn = n(−1)n, n ≥ 1 (a) Find Σ when 4 is on top, i=1 at the bottom and bi at the right hand side (b) Is b increasing, decreasing, non-increasing or non-decreasing?

Given ϕ2 = 5. Is ϕ increasing, decreasing, non-increasing and/or non-decreasing?

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1.Draw the digraph of the following relations. (a) R = {(1, 2), (2, 3), (3, 4), (4, 1)} on {1, 2, 3, 4} (b) R={(1, 2), (2, 1), (3, 3), (1, 1), (2, 2)} on X = {1, 2, 3}

For each relation below, determine if they are reflexive, symmetric, anti-symmetric, and transitive. (a) X= { 1, 2, 3, 4} R1={(1, 2),(2, 3),(3, 4)} (b) X = {a, b, c, d, e} R1 = { (a, a), (a, b), (a, e), (b, b), (b, e), (c, c),…

A discrete mathematics class contains I mathematics major who is a freshman, 12 mathematics majors who are sophomores, 15 computer science majors who are sophomores. 2 mathematics majors who are juniors. 2 computer science majors …

Use quantifiers and predicates with more than one vari- able to express these statements. a) There is a student in this class who can speak Hindi. b) Every student in this class plays some sport. c) Some student in this class has …

Create a schematic diagram of all odd numbers from 20 to 45

State whether the following graph g1 and g2 are isotropic or not

Find the conjunction of the propositions p and q where p is the proposition “Rebecca’s PC has more than 16 GB free hard disk space” and q is the proposition “The processor in Rebecca’s PC runs faster than 1 GHz.”

all swedish movies are serious

For each of the following compound propositions give its truth table and derive an equivalent compound proposition in disjunctive normal formal (DNF) and in conjunctive normal form (CNF). (a) (p → q) → r (b) (p ∧…

For each of the given statements: 1 - Express each of the statements using quantifiers and propositional functions. 2 - Form the negation of the statement so that no negation is to the left of the quantifier. 3 - Express the …

Translate these system specifications into English where the predicate S(x, y) is “x is in state y” and where the domain for x and y consists of all systems and all possible states, respectively. (a) ∃S(x, open) (b) ∀x(S(x…

(a) Find the inverse of 19 modulo 141, using the Extended Euclidean Algorithm. Show your steps.

A says “If B is a knight, then I am a knave”, B says nothing.

(e) Propositions 𝑝 and 𝑞 are defined on the universal set 𝑈 = {𝑞𝑢𝑎𝑑𝑟𝑖𝑙𝑎𝑡𝑒𝑟𝑎𝑙𝑠}. Let 𝑝 be the proposition “𝑥 is a square” and 𝑞 be the proposition “𝑥 is a rectangle”. If the implication is given as 𝑞 → 𝑝 , then state the conve…

Taking the long view on your education, you go to Econet Wireless Network Pvt Ltd and ask what you should do in university to be hired when you graduate. The personnel director replies that you will be hired only if you major in mathe…

Find the simplest form of given Boolean expressions using algebraic methods. i. A(A+B) + B(B+C) + C(C+A) ii. (A+|B|)(B+C) + (A+B)(C+|A|) iii. (A+B)(AC+A|C|)_+AB +B iv. |A|(A+B) + (B+A)(A+|B|)

b) Given p="Front door is open q="Back door is open" r="Light is on" s="The lift doors are open" t="The lift is moving", i) write the follow…

Detarmine whether each of these functions is a bijection from R to R

Find these values ⌊−3.1⌋

Detarmine whether each of these functions is a bijection from R to R

Let A= {1, 2, 3, 4}, and let R And S be the relations on A As follow: R = {(1,1),(1, 4),(3,2),(4,2),(4,3)} S = { (1,1),(1,2),(2,2),(3,3),(4,2),(4,4)) Then find out: 1. M𝑅𝑐 2. 𝑀𝑠̅ 3. M (𝑅∪ S)

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2. What does it mean for two propositions to be logically equivalent?

5. Let p be the proposition “I will solve every question in this assignment” and q be the proposition “I will be fully prepared for upcoming topics” Express each of these as a combination of p and q. a. I will be fully prepared for up…

3. Give an example of a predicate P(x,y) such that ∃x∀yP(x,y) and ∀y∃xP (x, y) have different truth values.

4. Suppose that a statement of the form ∀xP(x) is false. How can this be proved?

1. Let R be the relation on the set {0, 1, 2, 3} containing the ordered pairs (0, 1), (1, 1), (1, 2), (2, 0), (2, 2), and (3, 0). Find the a) reflexive closure of R. b) symmetric closure of R. 2. Find the t…

4. Which of these relations on {0, 1, 2, 3} are equivalence relations? Determine the properties of an equivalence relation that the others lack. a) {(0, 0), (1, 1), (2, 2), (3, 3)} b) {(0, 0), (0, 2), (2, 0), (2, 2), (2, 3),…

Define a binary relation P from R to R as follows: for all real numbers x and y, (𝑥, 𝑦) ∈ 𝑃 ⇔ 𝑥 = 𝑦^2 . Is P a function? Explain.

1. Consider the K-Maps given below. For each K- Map i. Write the appropriate standard form (SOP/POS) of Boolean expression. ii. Design the circuit using AND, NOT and OR gates. iii. Design the circuit only by using • NAND gates if …

Let R={1,1),(1,2),(2,1), (2,1), (3,3), (4,1), (5,1)} define on set A= {2,3,4,5,6}

(a) Find the inverse of 19 modulo 141, using the Extended Euclidean Algorithm. Show your steps. (b) Solve the congruence 19x ≡ 7 (mod 141), by specifying all the integer solutions x that satisfy the congruence. ≡

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Let α, β be roots of the equation x^2− 3x − 1 = 0. For each nonnegative integer n, let y_n = α^n + β^n . Show that gcd(y_n, y_(n+1)) = 1 for each nonnegative integer n.

Determine if each statement is a proposition. If so, also determine its truth value. Read and follow instructions. Ok I answered the assignment. 2+3=5 Let x be 5, x+y=10. DLSU-CCS is in Quezon City.

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Question ID: mtid-5-stid-8-sqid-3218-qpid-1917