Determine which of these relations are reflexive. The variables x, y, x', y' represent integers. A. x∼yx∼y if and only if xy≥0xy≥0 \). B. x∼yx∼y if and only if x−yx−y is positive. C. x∼yx∼y if and only if x+yx+y is even. D. x∼yx∼y if and only if xyxy is positive. E. x∼yx∼y if and only if x+yx+y is odd.

Q: Define two relations R1 and R2 on set positive integers. R, = {(a,b)|a > b} and R2= {(a,b)|a? = b }.…

A: Composition of relation

Q: |Let A¡ = [i − 1, i] for all integers i = 1,2,3,4. Find the following. a. A₁. A₂- b. A₁ U A₂ U A3 U…

A: The given set Ai=i-1, i for all integers i=1, 2, 3, 4. We have to find, a) A1, A2, A3, A4 b)…

Q: Find the maximum value of a, x, +a,x, + .+ax to the condition that x +x, +. + x =1 for given…

A: We need to find the maximum value of a1x1+a2x2+a3x3+...+anxn to the condition that…

Q: Scanned.47thDetermine if the relation r CS CamScannegymmetric, antisymmetric or neither

A: The relation R is said to be symmetric if any ordered pair (x,y) ϵ R then the ordered pair…

Q: 5. Find all values of h so that is a linear combination of and 4. O h=0 only Oh= 2 only Oh=-2 only…

A: We need to find all values of h so that (h04) is a linear combination of (1-10) and (138) to do that…

Q: Which of the following are true statements? State why. 2 E {1,2,3} b. {2} € {1,2,3} c. 2 C {1,2,3}…

A: # we are entitled to solve three subparts at a time, please resubmit the other questions and other…

Q: Let an = an-1+ an-2 with ao = 0, a1 = 1. Show that an is even iff ( if and only if) n is a multiple…

A:

Q: 8. Which of the following number lines depicts the solution to - (x- 5)(x- 8) > 0? + R а. 1 3 5 7 9…

A:

Q: Activity 7.2. Even if we omit the negatives, the real numbers fail to satisfy the well-ordering…

A: Given that the set R+ of all positive real numbers fails to be well ordered.

Q: Show that if ax2 + bx + c = 0 for all x, then a = b = c =0

A: It is given that, ax2+bx+c=0 for all x,  To prove a = b = c = 0

Q: 11. If |A| = 3, how many relations are there on A?

A: Given A=3

Q: 3. Let A = {-1, –3, –5}, B = {a, B, 7}, C = {x, y, z}. Consider the relations R from A to B and S…

A:

Q: What conditions, if any, must be set forth in order for a + b to be equal to n(A U B)?

A:

Q: 2 4. Express 989 = 23 43 in the form x² + xy + 5y².

A: The given number is 989. The objective is to express the given number in the form of x2+xy+5y2.

Q: 3. Show that all integers n ≥ 2 can be expressed as 2x + 3y for some nonnegative integers r and y.

A: Mathematical induction is a proof technique used in mathematics to establish the truth of a…

Q: Determine the union X ∪ Y. Express them in interval notation. X = {x/x>-17 } and Y = {x/x<equal-10…

A: The union of two sets A and B is defined as the set of all the elements which lie in set A and set B…

Q: 6. If -2 determine all values of x and y for which A= A.

A:

Q: T T T F 29. If x and y are real numbers and x² < y² then x < y. F 30. Let A, B, C and D be sets with…

A: We have to check whether the given statement is true or false.

Q: Exercise 8. [1, 2.2.10] Show that F₂Q1v₂ [c] iff a Vv₂Qcv₂ Here Q is a two-place predicate symbol…

A: Given information:A first-order logic structure denoted as A.Q is a two-argument predicate symbol.c…

Q: Determine the union X ∪ Y. Express them in interval notation. X = {x/x>-17 } and Y = {x/x<equal-10…

A: Introduction: The number of elements carried by the operation and executing the results of a…