B. Let A = (a, b. c. d). Let R be the relation on A defined as follows: R= {(a, a), (a, b), (a, c), (b, b), (b. a). (C, a), (c, C), (d, d)) State, giving reasons, whether R is reflexive, symmetric, or antisymmetric. Attach File Browse My Computer

Q: Let A C B and let S be an equivalence relation on B. Prove that R = {(x,y) E A × A : (x, y) E S} %3D…

A:

Q: Let B = {a, b, c}and S is the relation on B such that S3 (а, a), (а, b), (b, с), (а, с), (с, с).…

A: Given the set B={ a,b,c } and the relation S on B such that S={(a,a),(a,b),(b,c),(a,c),(c,c)}

Q: The relation on Z × N defined by, (a, b) ~ (c, d) if ad bc.

A: The objective is to show that the relation a,b~c,d then ad=bc is an equivalence relation. To show…

Q: ist the ordered pairs in the relation R from A = 0, 1,2, 3, 4, B = 1,2, 3, 4, 5, where Ris defined…

A:

Q: Let a relation S be defined on A = {0, 1, 2, 3} as follows. S= {(0, 0), (0, 3), (1, 0), (1, 2), (2,…

A:

Q: Let R be a relation from Q to Q defined by R = {(a,b): a,b ∈ Q and a – b ∈ Z}. Show that:(i) (a,a) ∈…

A: i) Given that a ∈ Q  a-a=0 ∈ Z So, (a,a) ∈ R for all a ∈ Q (proved)

Q: List the ordered pairs in the relation R from A = 0,1,2, 3, 4, B = 1,2, 3, 4, 5, where R is defined…

A: A=0,1,2,3,4 B=1,2,3,4,5 a2=b

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

A: Given set is A = {a, b, c, d} and the relation R on set A is R = {(a, b), (b, b), (b, c), (c, a),…

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

A: R=1,2,2,1,2,3,3,4,4,1set=1,2,3,4

Q: Let S be the relation on the set R^2 defined by (x, y) S (w, z) if |x| + |y| = |w| + |z|. Prove or…

A: Definition of an Equivalence Relations: A relation R on a set A is an equivalence relation if…

Q: Let R be a relation on the set A = {x € Z:1 < x < 100} defined as follows: x R y if and only if x-y…

A: Equivalence relation

Q: Consider the relation R on Z defined by the rule that (a, b) E R if and only if a + 26 is even.…

A:

Q: Consider the relation R on the set {a,b,c,d,e,f} which is defined as follows: R={(a,a), (a,b),…

A:

Q: Let A = {0, 1, 3, 5, 7, 8} and R be a relation defined on A such that R= {(x , y)| 4 divdes (x –…

A: We are given the set A = {0, 1, 3, 5, 7, 8} and the relation R defined on A such that R = {(x, y)| 4…

Q: Let R be a relation over set A. Let A = {1,2, 3, 4, 5, 6} and let R = {(a, b) e A² : |a – b| > 3} a)…

A: A relation R on a set A which is a subset of  A×A is said to be reflexive if for any x∈A,x,x∈R.  A…

Q: Consider the relation S on N defined by uSy + 5|(y + u). Determine whether S is symmetric, reflexive…

A:

Q: Let R = { ( a,b ) | a,b ∈ Q and a − b ∈ Z } . Prove that R is an equivalence relation on Q

A:

Q: Let L be the set of all lines in a plane and R be the relation in L defined asR = {(L1, L2) : L1 is…

A: The given relation R is defined as follows.

Q: Let R be the relation on Z defined by    R = {(a,b): a, b ∈ Z, a – b is an integer}.Find the domain…

A: R = {(a,b): a, b ∈ Z, a – b is an integer}. We know that the difference of two integers is always an…

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…

A: Here given that the set is A = {a, b, c, d} and the relation on A is given by R = {(a, c), (b, b),…

Q: Let X = {a, b, c}. Define a relation J on P(X) as follows: For all sets A and B in P(X), AJB A ANB #…

A: a) No  b) Yes  c) Yes

Q: Let T be the set of all triangles in a plane with R a relation in T given byR = {(T1, T2) : T1 is…

A: Given, Let T be the set of all triangles in a plane with R a relation in T given byR = {(T1, T2) :…

Q: Consider the relation on A = {a, b, c, d, e} given by R={(a,b),(b,c), (b,d),(b,e),(d,

A:

Q: Let R be a relation defined on Z as follows: (a,b) is an element of R if and only if the square of a…

A:

Q: List the ordered pairs in the relation R from A=0,1,2,3,4, B= 1,2,3, 4, 5, where Ris defined as (a,…

A: Given sets are: A={0,1,2,3,4} B={1,2,3,4,5} Relation R consist of those ordered pairs (a,b) such…

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…

A:

Q: Let A = {3, 5, 6} ,R relation on A defined by R = {(a, b) : a < b, a, b e A}. rit O a. {(5,3),…

A: If A= {3, 5,6} , Where R = {(a, b) : a&lt;b, a, b€A) } Find R?

Q: Let A={a.b.c.d.e) and S, T, U and V relations on A where S = {(a,g), (ab), (ba), (kd), (ce), (ed),…

A:

Q: Define a relation R on the set {1, 2, 3, 4} as follows: T = {(1, 4),(2, %3D 3),(2, 4),(4, 1),(2,…

A:

Q: Let R be the ternary relation on Z that is defined as R:= {(x,y, z) E Z × Z × Z : a² + y² + 2² < 5}…

A: If a relation is defined on Z, then the variables in the relation can have only integer values to…

Q: Let S be the following relation on ℂ: S = {(x, y) ∈ ℂ2 : y − x is real}. Prove that S is an…

A:

Q: Let R be the relation on a set {1,2,3,4,5} containing ordered pairs (1,1),…

A: A relation R is called reflexive on a set A if (x,x) is in R for all x in A. A relation R' is called…

Q: B. Let A = {1, 2, 3, 4}. Let R be the relation on A %3D defined as follows: R = {(1, 1), (1, 2), (1,…

A: Find if the given relation is reflexive, symmetric or antisymmetric.

Q: Show that the relation R in the set {1,2,3} given by R = {(1, 1), (2, 2),(3, 3), (1, 2), (2, 3)} is…

A:

Q: Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} issymmetric but neither…

A: Given, relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)}.

Q: Is anyone of the veetors e. 2-, ERa linear combination of the others? If so, find the relation(s)…

A:

Q: Let R be a relation on Z defined by xRy if and only if x-y=7k for kEZ. The equivalence class of [5]…

A:

Q: For (a, b),(c,d) EN×N define the relation (a, b) ~ (b,c) if and only if ab = cd. Is this relation…

A: Explanation of the answer is as follows

Q: Let R be a relation from A to B and S a relation from B to A. Prove or disprove that if S of R =…

A:

Q: Show that the relation R on Z defined by a R b if and only if 5a − 3b is even, for a, b ∈ Z, is an…

A: Given information: The relation R on Z defined by a relation b if and only if 5a − 3b is even, for…

Q: Let A= {2,3,4} B=  {6,8,10} Define relation R from A to B as follows;For all X,y

A: Given- A=2,3,4 and B=6,8,10 To Find- The relation R from A to B follows, for ∀∈x,y

Q: . Let R be the relation on Z→ Z such that ((a,b),(c,d)) eR = a+d =b+c. Show that R is an equivalence…

A: An equivalency relation on a set is a reflexive, symmetric, and transitive relationship for…

Q: Let R be a relation on the set A = {1,2,3,4,5, 6} defined by R = {(a,b) E A x A| a + b < 9}. a. List…

A: A ={1,2,3,4,5,6}

Q: Let R be the relation on the set {0, 1, 2, 3} containing the ordered pairs {(0, 1), (1, 1), (1, 2),…

A: To find the transitive closure of a relation, we just add the ordered pairs that completes the…

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…

A:

Q: Consider the relation on A = {a, b, c, d, e} given by R={(a,b),(b,c),(b,d),(b,e),(d,e)}

A:

Q: Let R be the relation on S = {a,b,c, d} given by the following digraph: b Then None of these R = (a,…

A:

Q: (a) Let R be the relation on Z defined as follows: For a, b e Z, a~b if and only if a is a multiple…

A:

Q: Let A = (0, 1, -1, 2} , R relation on A defined by R = {(a, b) : b= a², a, bE€ A}. Write R. %3D

A: Given ,  Let A = {0 , 1 , -1 , 2}  R relation on A defined by  R = {(a , b) : b = a2 , a , b € A} We…

Q: 2. Let R be the relation on Z→Z such that ((a,b),(c,d)) = R a+d =b+c. Show that R is an equivalence…

A: