Q1/ Let p:e N q: Thi-Qar is not in Iraq r:3 is a prime number are three propositions. Find the truth value of the following propositions 1.pA q 2. (p v-q) vr 3. If (paq) then (q v-r) 4. -(pq) A (rp) 5. Vx € N,x<-2
Q: 1. Given the following truth-value assignments, evaluate the following compound propositions. Make…
A: There are two expressions given, 1. (p -> q) ∧ (s <-> t) 2. (r⊕¬t) -> (¬p ∧ ¬s) We have…
Q: Let n be the product of two large primes. Alice wants to send a message m to Bob, where gcd(m, n) =…
A: Sol: Given n be the product of two large prime Alice wants to send a message m to bob gcd(m,n)=1…
Q: Let f(n) and g(n) be positive functions over the natural numbers. For each of the following claims…
A: Given asymptotic notation correct or disprove
Q: we know that P(A) = 1/4, that P(B) = 1/2, ar P(B|A) = 1/2, what is P(A|B) ? and that
A: Solution P(A/B)= 1/4 Conditional probability Probability of A happened given that B is happened…
Q: block u to obstruct v is a grouping u=x0→x1→x2→⋯→xk=v, where there is a street from block xi−1 to…
A: Here have to determine about the lengths over all streets programming problem statement.
Q: 6. Let a @b= max {a, b} = a if b ≤ a, otherwise a @ b = max {a, b} = b. Give a proof by cases that…
A:
Q: Let A = {x ∈ Z : x ≤ 3} and let B = {x ∈ Q : x2 = 9}. Is B ⊆ A? Give a brief reason for your answer.
A: True
Q: Let P(x) denote "x + 225", find the truth values for the following compound propositions: a) P (1) V…
A:
Q: Q-1: a) let p, q andr be propositions. Simplify the following compound proposition: (¬r) ^p^q) V…
A:
Q: Given the set of atomic propositions {p,q,r,s}, decide if any of the following is a proper…
A: An atomic proposition is a statement or assertion that must be true or false.
Q: (8) 4. Let Q(x) be the statement x + 1 = 2x. If the universe is the set of integers, what are the…
A:
Q: . Suppose H = {cat, dog, rabbit, mouse}, F= {dog, cow, duck, pig, rabbit} J = {duck, rabbit, deer,…
A: We are given 3 sets H,F,W and we are going to apply union and intersection operations on them which…
Q: Suppose n e Z. (That is, throughout this question, n is an arbitrary integer; you cannot pick a…
A: Given: P: If 7n+5 is odd, then n is even. Requirement: Find contrapositive of P
Q: Complete the truth table for (p v¬q) → ¬ (q^p) P 9 T T T F F T F F Is (pv¬q) + (q^p) a tautology,…
A: A tautology is an assertion of Propositional Logic that is true in all situations; that is, it is…
Q: Which of the following propositions is tautology O a. p ^ (-p V q) → -p O b. -p ^ (p V q) → p O c.…
A: The use of lexical items to convey a same thing in a different way in the same argument is known as…
Q: What type is inferred for a, ß, and for the variable xs? let xyz (a : a) : B %3D let rec abc a match…
A: Answer: I have given answered in the brief explanation
Q: Given p = T, q =T and r = F, find the truth value of the proposition given below.(p ngar)v(¬r)++(q →…
A: and operation will return False when at least one of the given proportions(p, q, r) is False, else…
Q: Proof that the following given propositions. 1. (p + r) A (q + r) - (p V q) + r 2. (p + q) v (p + r)…
A: A tautology is a mathematical assertion in which if the given proposition is said to be tautology…
Q: Let A = {c, e,j, 1, s, u, y, z}, which of the following is true? There may'be more than one correct…
A: A={c ,e ,j ,l ,s ,u , y, z} True answers are: A. Φ ⊆ A D. {l,y,s,u} = {u,s,l,y} E. {l,y,s,u} ⊆ A F.…
Q: (3) Use truth tables to determine whether the following set of sentences is consistent. { (K ·…
A: Given: use truth tables to determine whether the following set of sentences is consistent.
Q: Use the program truth.m and a modified version of propos.m to prove or disprove the following. [(p…
A: Answer is given below .
Q: The statement "There is a real number x such that for all real number y, xxy3D0". If O y)=xxy3D0,…
A: Objective: The mathematical notation for the statement should be chosen from the four alternates.…
Q: If P is a proposition, which of the following equivalence is valid? А. (Pv-P) = -(PA-P) (Pv-P) =…
A:
Q: According to some political pundits, a person who is radical (R) is electable (E) if he/she is…
A: Please keep in mind that we are only supposed to help with the first question if students ask for…
Q: 1. Big-O Notation Let fand g be functions from the set of integers or the set of real numbers to the…
A: Given that, f(x)= O(g(x)) that means f(x) is equal to big oh of g(x). Big-oh represents the tightest…
Q: Let P(x, y) denote the statement "x² >y-2", where x, y E Z. What is the truth value of each of the…
A: This can be read as For all x, there exists a y, for which "x2>y-2" is true. This is true,…
Q: buiddin Let the domain be the set of all positive integers. Let: P(x): "x is a perfect square".…
A: Given, P(x): "x is a perfect square" Q(x): " x is an even number" let's analyse if for x…
Q: 32. Which of the following proposition is the negation of (P→Q) ∨ ~Q? (P ∨ ~Q) ∧ Q (P ∧ ~Q) ∨ Q (P…
A: Given proposition is, (P→Q) ∨ ~Q P→Q can be written as ~P ∨ Q So, (P→Q) ∨ ~Q= (~P ∨ Q) ∨ ~Q If we…
Q: a) professor (Lucy) b) Vx (professor(x)= people(x)) c) dean (Fuchs) d) Vx (dean(x) = professor(x))…
A:
Q: Find g of (a) f:Z→ N, (b) f:R → (0,1), f(x)=1/(x² +1); f(n) = n² + 1; g:N → Q, g(n) = g: (0, 1) →…
A:
Q: In this group of problems, you are given the predicate P(x), where the domain of x is the set of…
A:
Q: when p and q are both true propositions while r is fale. which of the following has truth value of…
A: Here in this question we have given four Expression and given p=TRUE q = TRUE r=FALSE. we have to…
Q: Translate these statements into English: (Domain- all real numbers) I. Oy Vx (xy =y) II. Vx v y 3z…
A:
Q: Which of the following propositions is tautology? Select one: O a. p v (q→p) O b. None С. pv (р-9q)…
A: Which of the following propositions is tautology? Select one: a. pv (q→p) b. None c.pv (p→q)…
Q: Let p(n) 3+3-5+3 5++3-5-3(5+1-1)/4 a) What is the statement P(1)? b) Complete the inductive step of…
A: a) P(1) = 18 b) The statement is true for all natural numbers.
Q: Which of the following propositions is tautology? O (p v q)-q O pv (q-p) O pv (p-q) O p-q
A:
Q: Ex: Let A1 ={x, y}, A2 ={1, 2}, and A3 ={a, b}, (A1 x A2) x A3, A1 × A2 × A3. Find A1 x A2,
A: Given: Ex: Let A1 ={x, y}, A2 ={1, 2}, and A3 ={a, b}, Find A1 × A2=? (A1 × A2) × A3=? A1 × A2 ×…
Q: Let f(n) and g(n) be positive functions over the natural numbers. For each of the following claims…
A: Asymptotic notation of the given functions correct or disprove
Q: 1. Suppose H = {cat, dog, rabbit, mouse}, F = {dog, cow, duck, pig, rabbit} W = {duck, rabbit, deer,…
A: Suppose H = {cat, dog, rabbit, mouse}, F = {dog, cow, duck, pig, rabbit}, and W = {duck, rabbit,…
Q: all integers between -4 and 4, and the domain for y consists of all real numbers. Determine the…
A: As per the answering guidelines, solving first 3 sub question 1. There exists some x and for all y…
Q: Let M be the PDA defined by Q = {q, qo, ¶1, 92}, E= {a,b}, I' = {a}, F := {q , qı}. 8(9,, a , Zo) =…
A: For point b: Tracing computation in string aab: (q0,aab,Z0)|-(q,ab,Z0)|-(q,b,aZ0)|-(q1,e,Z0)=…
Q: hich of the following is the correct next step using laws of propositional gic? -(-p^q) AT =p V ¬q…
A: Here first we would need to remove the conjunction using conjunction elimination rule and use…
Q: Q3) Predict the following: h is a human and devil is not human p is peace and war is not peace…
A:
Q: Consider the following FOL sentence: PA Jx. (Q(x) ^ Vy.R(x, y)) Which one of the following formulas…
A: Skolemization: remove existential quantifiers by introducing newfunction symbols. How: For each…
Q: Simplify the following Boolean function by first finding the essential prime implicants: F(W, X, y,…
A: Given:
Q: 2. Let p, q, r be propositions. Based on given truth values of individual propositions or compound…
A: a) p XOR NOT q = T XOR T = F p -> r = NOT p OR r = F OR T = T Finally, F XOR T = T Hence True. b)…
Q: If p is true, q is false, r is true, and s is false, what are the truth values of ~(q ⇔ s) and ~r ⇔…
A: Lets see the solution.
Q: Questi Let f(x, y, z) = x² - y² + z, where x, y and z are positive integers. For each of the…
A: Since you have asked multipart question, we will solve only the first-three part of the question.…
Q: For the following f and pairs of fanctions state whichh of the relatiouships fE O(g) and /or fE o…
A: As per our guidelines, only 3 sub parts will be answered. So, please repost the remaining questions…
Q: Let f(n) = 2n and g(n) = n. a) Show that f is O(g) using specific values of C and no. b) Show that g…
A: Big-O Notation O(n): Let f(n) and g(n) be the two functions described and the function f is said to…
Step by step
Solved in 2 steps with 2 images
- 2) (L2) Prove using laws of logic that the conditional proposition (p ∧ q) → r is equivalent to (p ∧ ¬ r) →¬ q. 3) (L3) Show that the converse of a conditional proposition p: q → r is equivalent to the inverse of proposition p using a truth table. 4.1) (L4) Show whether ((p ∧ (p→q)) ↔ ¬p) is a tautology or not. Use a truth table and be specific about which row(s)/column(s) of the truth table justify your answer. 4.2) (L4) Give truth values for the propositional variables that cause the two expressions to have different truth values. For example, given p ∨ q and p ⊕ q, the correct answer would be p = q = T, because when p and q are both true, p ∨ q is true but p ⊕ q is false. Note that there may be more than one correct answer. r ∧ (p ∨ q) (r ∧ p) ∨ qAssume the propositions p, q, r, and s have the following truth values:p : False (F). q : True (T). r : False (F). s : True (T). Evaluate the truth value for each of the following compound propositions. Show your work for yourevaluation.a) (p ∨ q) ∧ ¬ rb) p ∨ q ∧ ¬ rc) ¬(r ∨ s) → p ∨ qd) r ⊕ ¬s ↔ q → pe) (p ∧ ¬q) ⊕ (r → (¬s ∨ q))5. Let R = {1, 3, π, 4, 1, 9, 10}, S = {{1}, 3, 9, 10}, T = {1, 3, π}, and U = {{1, 3, π}, 1}. Which of thefollowing are true? For those that are not, why not? (d) 1 ⊆ U(e) {1} ⊆ T(f) {1} ⊆ S(g) {1} ∈ S
- Algorithm to An iterative solution to Towers of Hanoi.in: triplet S = s0, s1, s2 representing the current game stateout: triplet R = r0, r1, r2 representing the new game statelocal: pole indices a, b, z ∈ {0, 1, 2}; disc numbers g, h ∈ [2, n]; last(Q) = Q|Q|−1, if1 ≤ |Q|, otherwise, last(Q) = +∞Determine whether the following proposition is a tautology: (¬p∨¬(r⟶q))⟷(p⟶(¬q∧r)) can i get a non handwriting answer so it would be easy to copy pleasewhen p and q are both true propositions while r is fale. which of the following has truth value of false? 1. p v q v ¬ r 2. (p -> q) ^ ¬ r 3. p v q v r 4. ¬ r-> ¬ (p ^q)
- Prove or disprove that the two propositions in each pair are equivalent. (p (q r)) , ((p q ) ( p r )) (p (q r)) , (( p q ) ( p r )) (( p q ) r ) , ( p ( q r))The converse and the inverse of a conditional statement are equivalent Select One True False Let p, q, and r be propostions with the truth values (True, False, False) respectivly, then the truth value of the propositional statement (¬p ↔️ ¬q) ↔️ (q ↔️ r) is Select One True False The biconditional statement p ↔️ q and the statement (p → q ) ∧ (q → p) have different truth values Select One True False Determine whether the following propositions is true or false. if 1+1=3, then 2+2=4 Select One True False Determine whether the following propositions is true or false. 2+1=3 if and only if 5Consider the problem of making change for n cents using the fewest number of coins. Assume that we live in a country where coins come in k dierent denominations c1, c2, . . . , ck, such that the coin values are positive integers, k ≥ 1, and c1 = 1, i.e., there are pennies, so there is a solution for every value of n. For example, in case of the US coins, k = 4, c1 = 1, c2 = 5, c3 = 10, c4 = 25, i.e., there are pennies, nickels, dimes, and quarters. To give optimal change in the US for n cents, it is sufficient to pick as many quarters as possible, then as many dimes as possible, then as many nickels as possible, and nally give the rest in pennies. Design a bottom-up (non-recursive) O(nk)-time algorithm that makes change for any set of k different coin denominations. Write down the pseudocode and analyze its running time. Argue why your choice of the array and the order in which you fill in the values is the correct one. Notice how it is a lot easier to analyze the running time of…
- Consider the problem of making change for n cents using the fewest number of coins. Assume that we live in a country where coins come in k dierent denominations c1, c2, . . . , ck, such that the coin values are positive integers, k ≥ 1, and c1 = 1, i.e., there are pennies, so there is a solution for every value of n. For example, in case of the US coins, k = 4, c1 = 1, c2 = 5, c3 = 10, c4 = 25, i.e., there are pennies, nickels, dimes, and quarters. To give optimal change in the US for n cents, it is sufficient to pick as many quarters as possible, then as many dimes as possible, then as many nickels as possible, and nally give the rest in pennies. Design a bottom-up (non-recursive) O(nk)-time algorithm that makes change for any set of k different coin denominations. Write down the pseudocode and analyze its running time. Argue why your choice of the array and the order in which you ll in the values is the correct one.Consider the problem of making change for n cents using the fewest number of coins. Assume that we live in a country where coins come in k dierent denominations c1, c2, . . . , ck, such that the coin values are positive integers, k ≥ 1, and c1 = 1, i.e., there are pennies, so there is a solution for every value of n. For example, in case of the US coins, k = 4, c1 = 1, c2 = 5, c3 = 10, c4 = 25, i.e., there are pennies, nickels, dimes, and quarters. To give optimal change in the US for n cents, it is sufficient to pick as many quarters as possible, then as many dimes as possible, then as many nickels as possible, and nally give the rest in pennies. Prove that the coin changing problem exhibits optimal substructure. Design a recursive backtracking (brute-force) algorithm that returns the minimum number of coins needed to make change for n cents for any set of k different coin denominations. Write down the pseudocode and prove that your algorithm is correct.H. Determine the truth value of the following proposition1. If Microsoft is partly-owned by Bill Gates, then dogs are amphibians.2. MERALCO is an electric company and 3 is less than 5.3. Cigarette smoking causes cancer or COBOL is a programming language.4. Pentium III is a processor if and only if Venus is a planet.5. Antarctica is a continent if chocolate is sweet.6. Indonesia is the largest archipelago or 2 + 2 = 5.7. Snakes are reptiles and elephants are small animal.8. Ostrich is not a bird.