Suppose that R1 and R2 are symmetric relations on a set A. a) Is R1 U R2 also reflexive? Is R1 ∩ R2 also reflexive? Explain.

Q: 6. Consider the relation R = {(a, b), (a,c), (c, b), (b,c)} on the set A = {a, b,c}. Which of the…

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Q: Let R be the relation defined on P({1, . . . , 100}) by A R B    if and only if |A ∪ B| is even.…

A: Relation on a set

Q: Determine whether the given relation is reflexive, symmetric, transitive and an equivalence…

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Q: Check whether R is reflexive, symmetric or transitive and hence determine whether the relation R is…

A: The given relation is not an equivalence relation. First check if the relation R is reflexive.…

Q: prove why each relation has or does not have the properties: reflexive, symmetric, anti-symmetric,…

A: The given relation R is as follows. R=x,y∈Z×Z:x is a multiple of y If x,y∈R, we denote x related to…

Q: Determine whether the given relation is reflexive, symmetric, transitive and an equivalence…

A: By definition of  relation it is define as A relation is symmetric if and only if (b, a) ∈ R…

Q: Consider the relation R = {(1, 2),(2, 1),(2, 3),(3, 4),(4, 1)} on {1, 2, 3, 4}.Is R reflexive?…

A: In this question we have to explain Is the given relation is reflexive.

Q: Which relation on the set {a, b, c, d} are equivalence relations and contain(i) (b, c) and (c, d)

A: The set {a, b, c, d}.

Q: Let S be the set of ordered pairs of positive integers, and define (a,b) R (c,d) to mean that 2a-d =…

A: A relation R is transitive on a set A if xRy and yRz then xRz for all x,y and z belong to A. Now,…

Q: What is the reflexive closure of the relation R = {(a, b) | a > b} on the set of integers? Select…

A: Reflexive Relation Definition:  A reflexive relation is the one in which every element maps to…

Q: Describe the equivalence classes of the relation R = {(a, b) : a € Z, b E Z, 13 divides (a – b)}

A: a equivalence class is a subset of the set on which the relation R is defined such that all elements…

Q: Đ A is a closed set.

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Q: Consider the following relation R on the set Give an example of a pair that is not in R, but in the…

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Q: 4. Let R and S be relations defined on the set A. If both R and S are symmetric relations, are: a) R…

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Q: Check if the following statement is TRUE or FALSE. Let R be an equivalence relation on a nonempty…

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Q: let R be the relation on the set of positive integers in which a R b if and only if a is a factor of…

A: Given below the detailed Solution.

Q: Consider the relation R = {(a, b), (a, c), (c, c), (b, b), (c, b), (b, c)}. Is R reflexive,…

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Q: VIII.3. Is there a mistake in the following proof that any transitive and symmetric relation Ris…

A: Yes there is a mistake. That Symmetric and transitive relation doesn’t imply reflexive. in the…

Q: Let R be the relation on the set of real numbers such that a R b if and only if a – b is an integer.…

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Q: Determine whether the following statements are True or False: Part A: Suppose R1 and R2 are…

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Q: Check the following relation R on the set A = {1,2, 3, 4} is reflexive, symmetric and or transitive…

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Q: Determine if the relation R = {(1,3), (1,4), (2,3), (2,4), (3,4)} is reflexive, symmetric,…

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Q: Check whether the relation R in R defined by R = {(a, b) : a ≤ b3} is reflexive, symmetric or…

A: The given relation R is defined as follows.

Q: Determine the following relation on the set {a, b, c, d}, is reflexive, irreflexive, symmetric,…

A: Let R represent a relation on a given set S=a,b,c,d. Then, relation R is said to be reflexive; if…

Q: Consider the six relations on a set of real numbers given below R1 = {(a, b) e R2 | a > b}, R2 =…

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Q: ( Prove that the set {a E R2: a2 ... Prove that the set {a E R2: a2 not equal to 6} is open.

A: Let the set is A=a1,a2∈ℝ2:a2≠6 The objective is to prove that the set A is open.

Q: Which of these relations on the set of integers is reflexive ? O R2 = {(a, b) i a -b or a = -b} O R4…

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Q: Describe the equivalence classes of the relation R = {(a, b) : a E Z,beZ, 13 divides (a - b)}

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Q: Let Z = {1,2, 3, ...,50}. a. How many relations on the set Z are both reflexive and antisymmetric?…

A: Here given set Z=1, 2, 3, ....., 50

Q: Check the following relation R on the set A = {1,2,3, 4} is reflexive, symmetric and or transitive…

A: Relation R on set A = {1, 2, 3, 4} and R is defined as, a,b ∈ R if and only if a≠b,∀a,b∈A.

Q: Let R be the relation on the set of integers such that a R b if and only if a = b or a = - b.…

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Q: Consider the relation R = {(1, 2), (2, 1), (2, 3), (3, 4), (4, 1)} on {1, 2, 3, 4}. Is R…

A: Definitions: Suppose R is relation defined on a set X then  i) R is reflexive if xRx, ∀x∈X. ii) R is…

Q: Let R be the relation on set {a,b,c,d} containing ordered pairs (a,c),(b,b),(b,a)(c,a)(c,d) and…

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Q: Check the following relation R on the set A = {1, 2, 3, 4]} is reflexive, symmetric and or…

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Q: 3. Let S = R × R and R be the relation on S defined by (a, b)R(c, d) iff a+c=b+d. Determine whether…

A: Reflexive: (x,y) R (x,y) As x+y=x+y Symmetric : if (a,b)R(c,d) then a+b=c+d. Since c+d=a+b then…

Q: Let the relation R on the set of ordered pairs of positive integers be defined as (a, b) R (c, d) a,…

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Q: '17. Prove or disprove: Let R be an equivalence relation defined on a set A. For any x, y E A,…

A: Given result is: '' Let R be an equivalence relation defined on a set A. For any x,y∈A, either x∩y=∅…

Q: etermine whether the relation R on the set of all people is reflexive, symmetric, antisymmetric,…

A: Note: We will only answer up to three sub-parts as the exact one is not specified. Please resubmit…

Q: Consider the relation R = {(1, 1), (1,3), (2,4), (3, 1), (3,3), (4, 3),(4,5)} on the set A =…

A: Let R be a binary relation on a set A. R is said to be  reflexive if for all . R is said to be…

Q: Let ℝ denote the set of real numbers, and  β:={(x,y)∈ℝxℝ| xy≥∅} be a relation on ℝ. Which…

A: The given relation β⊂ℝ2 is: β=x,y∈ℝ×ℝ | xy≥0 The properties of a relation is: Reflexive Irreflexive…

Q: (a) Explain what it means for a relation R on a set S to be (i) reflexive; (ii) symmetric; (iii)…

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Q: 3. Let R be the relation defined by x R y + x² <y? Determine ifR is an order relation on N? on Z?…

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Q: Let R be a relation defined on the set Z by aRb if a < b. What property/properties are violated? *…

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Q: R How to prove that " If is the equivalence B relation on the set and is the function R = IB then

A: given in question R is a equivalence relation on set B that means R is reflexive ,transitive  and…

Q: Check the following relation R on the set A = {1,2, 3, 4} is reflexive, symmetric and or transitive…

A: Not reflexive.  Symmetric.  Transitive.  Not Equivalence relation.

Q: let A= {a,b,c,d} and R= {(a,a),(a,c),(b,d),(c,a),(c,c),(d,b)} be a relation on A. What is the…

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Q: Consider the relation R = {(1, 1), (1,3), (2,4), (3, 1), (3,3), (4, 3)} on the set A = {1,2,3,4,5}.…

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Q: prove why each relation has or does not have the properties: reflexive, symmetric, anti-symmetric,…

A: Step 1:   The given relation is defined as:

Q: Let A be {a,b,c}. Let the relation R be AxA-{{b,a),(c,b)}. Which of the following statements about R…

A: In first question, first option is correct.