а) The relation R on A = {3, 5, 7, 9} is defined by the ordered pairs below: R= {(3, 3), (3, 9), (5, 3), (5, 7), (7, 3), (7, 9), (9, 3), (9, 5), (9, 9)} Does the relation R have reflexive, irreflexive, symmetric, asymmetric, antisymmetric or transitive properties? Give a counterexample if the answer is “No".

Q: (2 1). If Let vi = 1 2 2 is ,V3 V4 3 a dependence relation on (v1, v2, V3, V4) thenx = a) 17 b) 15…

A: Here, we have v1=111, v2=123, v3=321, v4=210. If xy-1-3 is a dependence relation on v1, v2, v3, v4,…

Q: • if Rit is a symmetrical relationship then R-1 is not symmetrical False O true نقطة واحدة • ifA =…

A:

Q: R and S are relations on set A = {1,2,3,4}, defined as R = {(1,2},(1,3),(2,3),(2,4),(3,1)}; S =…

A:

Q: Let ∼be the relation on Z defined as follows: For every m, n ∈Z, m ∼n if, and only if, 5 | (m2 −n2…

A: (a) For every m ∈ Z, 5 | (m2 −m2) = 0      Hence, m ~ m for all m ∈ Z      Hence, ~ is reflexive.

Q: Which of these relations on the set {0, 1, 2, 3} are equivalence relations? Determine the…

A:

Q: Q4) Find the following: 1- Find the relation Z from C to X where C = {1, 2, 3, 5} and X = {4, 6, 9}.…

A: Here, C=1,2,3,5X=4,6,9

Q: Suppose that f : A → B is a function, viewed as a relation (set of ordered pairs). Let f* denote the…

A:

Q: 2 Explain why the relation on N defined as is not an equivalence relation. {(x,y): +y is a multiple…

A:

Q: Give a specific reason why the following set R does not define an equivalence relation on the set…

A: We will find out the required value.

Q: The relation…

A: Given: R is a relation from A to A such that A=1,2,3,4,5 &…

Q: Let R be a relation on a set A Let R' be the relation on A defined by Graph(R') = (A × A) –…

A:

Q: Let R be an equivalence relation on A = {0, 1, 4, 5, 7, 9} and R = {(0, 9), (9, 0), (0, 0), (9, 9),…

A:

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: A relation ~ is defined on the set of all pairs of integers by the formula (m,n) ~ (u,v) m - An =…

A:

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

A: Given set is A = {1, 2, 3, 4, 5} and relation is R = {(1, 1), (1, 2), (2, 2), (2, 5), (3, 1), (3,…

Q: 3. Which graph models the relation {(2, 1), (1, 2), (1, -2)}?

A: Given: The relations is {(2,1) , (1,2) ,(1,-2)}  which gives that 2→1     ⇒(2,1)1→2    ⇒(1,2)1→-2…

Q: Let R=}(x,y)|2 divides 8x+by} be a relation the Set H= {1, 2,3.4,5, 6. 10 Determine whether the…

A:

Q: How many (distinct) equivalence classes does the relation R-(1.1), (2.2) (3,3),(4,4), (1,2), (2.1).…

A: The relation is R=1,1,2,2,3,3,4,4,1,22,1,3,4,4,3 The set is X=1,2,3,4

Q: 22) (a) Show that the relation {(0,0), (1,1),(1,2), (2,1), (2,2), (3,3)} is an equivalence relation…

A: Given 0,0,1,1,1,2,2,1,2,2,3,2

Q: V = Span{(1, 2, 3), (1, 0, 2)} and W = Span {(0, 2, 1), (1, 1, 1)}. Find the relation between V and…

A:

Q: Given the relation R = {(1,2),(2,3)} on the set A = {1,2,3} . What is the minimum  number of ordered…

A:

Q: Q2. (a) Find the equivalence class [-3]5 (b) Find the ordered pairs of the relation R from the set A…

A: We have to answer the following questions :  (a) Find the equivalence class  -35 (b) Find the…

Q: 7. (Relations) Consider the set A= (1,2, 3, 4, 5), and a relation R defined by zRy -y is an integor…

A: Given, A = 1, 2, 3, 4, 5xRy ⇔x2-y is an integer multiple of 3.

Q: What are the equivalence classes of the equivalence relations on {0, 1, 2, 3}?

A: Answer:-  Find the equivalence classes of the equivalence relations on A = {0, 1, 2, 3}?

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

A: We know: Symmetric closure of a relation R, △, is obtained by adding (b, a) to R for each (a, b) ∈ R…

Q: Let A = {1,2,3,4} and let R = {(1,1),(1,2),(2,1),(2,2),(3,4),(4,3),(3,3),(4,4)} . Show that R is an…

A:

Q: A// Which of these relations on {0, 1 , 2, 3 } are equivalence relations, why? a) R1= {(0, 0). (1 ,…

A: According to our guidelines we can answer only first question and rest can be reposted.

Q: Let X = {a, b, c, d, e,f} and S be the relation on X defined by S = || {(а, а), (а, b), (а, с), (а,…

A:

Q: There are 6 towns {A, B, C, D, E, F} with the following one way street relation {(A, B), (A, C), (B,…

A: