(a) Show that the following sentence -Vx(3yR(x, y) = R(x, f (1, 2)))is satisfiable where f is a 2-place function symbol and Ris a 2-place relation symbol.4.(b) Show that there is a derivation of - (x = y = (y = z = x = z)).

Answered: (a) Show that the following sentence…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let R be the relation on R defined by Ry if and only if ry 1. Thus R can also be represented as (r, y) ry = 1} . Use a similar representation for each of your answers to the questions below, and write your answer in the accompanying box What is the composite relation R2 ? (a) (b) What is the composite relation R3? What is the composite relation R4? (c) (d) What is the transitive closure of R?
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If an expoential relation such as y=bx, if b > 0 and b ≠ 1, then the y intercept is at zero. Is this true or false?
Determine whether the following relation is an equivalence relation or not. (à) G = {(x, y) |x divides y} (b) G = {(x, y) |x y or x = -y}
4. Use first or second differences to determine the type of relation between x and y. 5 -1 2. 1 4. a) linear b) neither linear nor quadratic c) quadratic d) unable to determine 5. The graph of the quadratic relation y = x - 3x – 4 is shown below. For what value or values of x is y = 0? 5. a) x= -1 only b) x= -1 and x = -4 c) x = -4 only d) x= -1 and x = 4 6. The graph of y = x* is translated 3 units to the right. The equation for this new graph is 6. a) y=x² +3 b) y= 3x? c) y =x³ -3 d) y = (x-3)? 7. Decide which direction the graph of y = -x -6 opens, its vertex point, and what its translation from y =x is. 7. a) opens down, vertex at (0, -6), shifted b) opens down, vertex at (-6, 0 ), shifted down 6 units up 6 units c) opens up, vertex at (0, -6), shifted up 6 d) opens up, vertex at (-6,0), shifted units down 6 units 8. Which of the following equations represents an exponential relation? (Ready for Gr.11!? O) 8. a) y=x? b) y=x c) y= 6" d) y =x³ + 2x2 – 5x +1
Show that if for a relation R we know that R^2 ⊆ R, then R is transitive, and conversely.
Decide whether the following relations is an equivalence relation or not. {(x, y) | xy > 0, x and y are integers}
Give examples: For each of the four relations between natural numbers x and y in the left column of the table below, and each of the three properties of relations in the top row, indicate whether the given relation has the given property. Write yes or no in each cell. {(x,y) | x <- N, y <- N, relation}reflexivesymmetrictransitivex /= y x >= y x + y >= 10 even (x + y)
The relation R is defined in A = {1, 2, 3} by a R b if |a² − b²| ≤ 5. Which of the following is false? Select one: a. R¹ = R O b. Range of R = {5} c. Domain of R = {1, 2, 3} 2 R1 O d. e. R={(1,1),(2, 2), (3, 3), (2, 1), (1, 2), (2, 3), (3, 2)}

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(a) Show that the following sentence ¬Vz(3yR(x,y) = R(x, f(x, x)) is satisfiable where f is a 2-place function symbol and Ris a 2-place relation symbol. 4.