Order the following sentences so that they form a direct proof of the statement: If x and y are rational numbers, then 3x + 2y is also a rational number. Choose from this list of sentences Since b, d are integers, bd is an integer. By the definition of rational numbers, x = alb where a and b are integers and b 0, and y = c/d where c and d are integers and d 0. Since 3x + 2y can be expressed as a ratio of two integers where the denominator is not zero, 3x + 2y is a rational number. Since a, b, c, d are integers, 3ad + 2bc is an integer. Let x and y be rational numbers. Since b 0 and d # 0, bd # 0. It follows that 3x + 2y = 3a/b + 2cld = (3ad +2bc)/(bd) Direct proof of the statement (in order):

Order the following sentences so that they form a direct proof of the statement: If x and y are rational numbers, then 3x + 2y is also a rational number. Choose from this list of sentences Since b, d are integers, bd is an integer. By the definition of rational numbers, x = alb where a and b are integers and b 0, and y = c/d where c and d are integers and d 0. Since 3x + 2y can be expressed as a ratio of two integers where the denominator is not zero, 3x + 2y is a rational number. Since a, b, c, d are integers, 3ad + 2bc is an integer. Let x and y be rational numbers. Since b 0 and d # 0, bd # 0. It follows that 3x + 2y = 3a/b + 2cld = (3ad +2bc)/(bd) Direct proof of the statement (in order):

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Let the following statements be given. p= "You can vote." q = "You are under 18 years old." r = "You are from Mars." (a) Translate the following statement into symbols of formal logic. You can't vote if you are under 18 years old or you are from Mars. O (q vr) → p O¬p → (q^r) O (q^r) → p O (qvr) → p O¬p → (qVr) (b) Give the contrapositive of this statement in the symbols of formal logic. Op (q^r) O¬¬p → ¬(q V r) O¬p → ¬(q Vr) (q V r) → O(g ^r) → p p (c) Give the contrapositive in English. O If you are under 18, then you can't vote nor are you from Mars. O If you are not under 18 nor are you from Mars, then you can't vote. O If you can't vote, then you are not under 18 nor are you from Mars. O If you can vote, then you are not under 18 nor are you from Mars. O If you are not under 18 nor are you from Mars, then you can vote.
Q. There is an island that has two kinds of inhabitants, knights, who always tellthe truth, and their opposites, knaves, who always lie. It is assumed that every inhabitant of theisland is either a knight or a knave. Below there are 3 inhabitants, who are denoted by A, B andC.A. What are A, B and C if A says “If B is a knave then C is a knave”, and B says “If Cis a knight then A is a knave”? Briefly explain your reasoning.B. What are A,B and C if A says “B is a knight and C is a knight”, and B says “A is aknight if and only if C is a knave”? Briefly explain your reasoning.
Conway's Game of Life: This is a zero person game with the following rules: (see Wikipedia for example) Any live cell with fewer than two live neighbours dies, as if by underpopulation. Any live cell with two or three live neighbours lives on to the next generation. Any live cell with more than three live neighbours dies, as if by overpopulation. Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction. Remember the oscillator or blinker of 3 cells. You can also find this blinker on Wikipedia. 1 21 1 2 1 21 3. 4 6 4. 6. 4 8. 9 8 9 #1 #2. #3 5. Consider now these 3 creatures at stage 1: Show how they look like in the next two stages: stage 2 and stage 3. Explain how you get the answers Creature 1 Creature 2 Creature 3 (here creature 1 is the blinker of 3 cells, horizontally; creature 2 consists of two adjacent cells, creature 3 consists of 4 adjacent cells horiztonally) ww (d) Creature 1 (10%), (e) Creature 2 (8%), (f) Creature 3 (20%)
Let M(x) = "x passed the midterm". Let F(x) = "x passed the final". Select the statement below which means: "If nobody passed the midterm, then everyone passed the final". Vx-M(x)→ VxF(x) Vx(M(x)→ F(x)). +VæM(z) → VF(x) Vx(-M(x) → F(x))
Note that for this question, you can in addition use ``land'' for the symbol ∧ ``lor'' for the symbol ∨ ``lnot'' for the symbol ¬``is_not'' for the symbol≠. Consider a tiny Robot World (robot R in a room) which has two actions:walkout: R walks out of the roomunlock: R unlocks the door. two fluents:DoorLocked: the room door is locked,InsideRoom: R is inside the room. a) R can walk out of the room iff R is inside the room and the door is not locked. Meanwhile, R can unlock the door if it is locked. Write the precondition axioms for these two actions. b) Consequence of the action walking-out is that the fluent InsideRoom becomes false. Consequence of the action of unlocking is that DoorLocked is false. Assuming explanation closure, write the successor state axioms for these two fluents. c) If in the initial state S0, we have both fluents (DoorLocked, InsideRoom) true, would the following sequence of actions a legal one?do(walkout, do(unlock, S0))If yes, what would be the fluent values in…
Suppose P and Q are the statements: P: Jack passed math. Q: Jill passed math. (a) Translate “Jack and Jill both passed math” into symbols. (b) Translate “If Jack passed math, then Jill did not” into symbols. (c) Translate “P ∨ Q” into English. (d) Translate “¬(P ∧ Q) → Q” into English.
Suppose that p and q are statements so that p → q is false. Find the truth values of each of the following. (a) ~p → q TrueFalse (b) p ∨ q TrueFalse (c) q → p TrueFalse
Let D = {-1, -2, -3} and E = {−3, 1, 2, 3, 5}. Write negations for each of the following statements and determine if the given statement is true or its negation. Explain your answer. (i) V E D, ³y € E such that x + y = 0. (ii) ay € E such that vx € D, x + y ≥ 2. (iii) vy € E, 3x = D such that xy ≥ 0.
Let A and B be sets such that ACB. Consider the following statements: (1) If A is finite, then B is finite. (2) If A is infinite, then B is infinite. (3) If B is finite, then A is finite. (4) If B is infinite, then A is infinite. Which of the following is true? Statements (1) and (2) are true. Statements (1) and (3) are true. Statements (1) and (4) are true. Statements (2) and (3) are true. Statements (2) and (4) are true. Statements (3) and (4) are true. None of the above is correct.
Consider the following statements: T(x. y): "x eats y". A(x): "x is wise". S(x): "x is hungry". F(y): "y is fat". H(y): "y is healthy". The domain of x is the set of all people and the domain of y is the set of all food. Select the symbolic of the following sentence (one or more answers): "All healthy food are eaten by all wise people" O vx Vy -T(x,y) V ¬A (x) V ¬H(y) O vx Vy -T(x,y)A (x) V H (y) O Vx Vy T(x.y)- ¬A (x) V -H(y) None of all proposed answers O vx Vy -T(x.y) -A (x) V -H(y)
Correct answer will be upvoted else downvoted. Computer science. You are given a positive integer x. Check whether the number x is representable as the amount of the solid shapes of two positive integers. Officially, you really want to check in case there are two integers an and b (1≤a,b) to such an extent that a3+b3=x. For instance, in the event that x=35, the numbers a=2 and b=3 are reasonable (23+33=8+27=35). In the event that x=4, no pair of numbers an and b is reasonable. Input The primary line contains one integer t (1≤t≤100) — the number of experiments. Then, at that point, t experiments follow. Each experiment contains one integer x (1≤x≤1012). Kindly note, that the input for some experiments will not squeeze into 32-cycle integer type, so you should use something like 64-bit integer type in your programming language. Output For each experiment, output on a different line: "Indeed" in case x is representable as the amount of the 3D shapes of two…
Click and drag the appropriate word, symbol, or phrase into the most appropriate blank. Let P(x) be the statement "x can speak Russian" and let Q(x) be the statement "x knows the computer language C+t." Consider the statement, "Every student at your school either can speak Russian, or knows C+." This statement is k(n) beginning of the symbolic statement is statement, because of the word, "every." So, the appropriate quantifier to be applied at the .We want this symbol to act on x, representing a student at your school. The universal statement may be rewritten for clarity's sake as, "Every student at your school speaks Russian or every student at your school knows C++." The phrases, "student at your school speaks Russian" and "student at your school knows C++" are directly symbolized by respectively. Finally, the word "or" requires the statement to employ the . Hence, the completed quantified statement is Q(X) and P(x) P(x) and Q(x) universal VX(P(x)vQ(x)) 3X(P(X)AQ(x)) conditional…