4. Let R and S be relations defined on the set A. If both R and S are symmetric relations, are: a) R nS also symmetric relation? b) R US also symmetric relation?

Q: Let A = { 2, 3, 4 } and B = { 6, 8, 10, 12 } and define a relation R from A to B as follows: %3D For…

A:

Q: In Q1-Q4 prove why each relation has or does not have the properties: reflexive, symmetric,…

A: Since you have asked  multiple questions so as per guidelines we will solve  the first question for…

Q: Let R be a relation from N to N defined by R = {(a, b) : a, b ∈N and a = b2}. Arethe following…

A: Let R be a relation from N to N defined by R = {(a, b) : a, b ∈N and a = b2} (i) But Therefore,

Q: Let A = {a,b, c, d, e, ƒ}, and let G and H be the following equivalence relations in A: G = IA U…

A:

Q: Given the relation R = {(u,t),(v,t),(w,t),(w,u),(w,v)} on a set A = {t,u,v,w}, what is/are the…

A: topic - relation

Q: Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} asR = {(a, b) : b = a + 1} is…

A: Given, relation R defined in the set {1, 2, 3, 4, 5, 6} as R = {(a, b) : b = a + 1}.

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: Identify the relation on set (1,2,3,4} if it is reflexive, symmetric, antisymmetric or transitive.…

A: We know that , relation is relationship between sets of values. A binary relation R defined on set A…

Q: Given the relations on the set of real numburs, &, - E(G,6) ER; a>b3, Rq = {CaL) EE, az6} Rs ={(a14)…

A: GivenR1=a,b∈R2 , a>bR2=a,b∈R2,  a≥ba) we know that R1+R2 contains thoseelements which are either…

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 R be a transitive relation on set A. Define Q to be {(r Prove or disprove that (RUR®)n (QU Qº)…

A:

Q: Use the Ruler axiom to prove that there is a one-to-one correspondence between any two lines.

A:

Q: Suppose R and S are relations on {a, b, c, d}, where R = {(a, b), (a, d), (b, c), (c, c), (d, a)}…

A: we have given relations R and S on {a, b, c, d} and we need to find composition R∘S

Q: We defined the relation between sets by A ~ B means that there there is a 1-1 correspondence ƒ : A →…

A: We define the relation ~ between sets by A~B means that there is a one-one correspondence f:A→B Show…

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

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: 6f) For the set X = {m,n, p, q,r, s}, let R be a relation on P(X) (the power set of X), given by A R…

A: Yes , this is correct. The set X= {m, n, p, q, r, s} |X|=6 The power set P(X)={ {}, {m}, {n},…

Q: Let A = {a, b, c} and B = {r, s, t,u}. Furthermore, let R = {(a,s), (a, t)}, (b, t) be a relation…

A: Step:-1 Given that A=a, b, c,  B=r, s, t, u And R=a, s, a, t, b, t that is,  Hence,  Domain of R =…

Q: Let A = {0, 1, 2} and B = {0, 8, 9}. If R is the relation from A to B such that (a, b) ∈ R provided…

A: If ab=0 then either a or b is equal to 0 Both also can be 0.

Q: Let R = { ( a, b ), ( a, d ), ( b, d ), ( c, a ), ( c, c ), ( d, b ), ( d, c ) } be a relation on…

A: Given: R=a,b,a,d,b,d,c,a,c,c,d,b,d,c   The relation R2 contains all ordered pairs (x, z) if (x, y)…

Q: Let R = { (1,1), (3,1), (2,1),(2,2), (1,3) } be a relation on the set A = {1,2,3}. Construct a…

A: The set A×A={(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)} R={(1,1), (3,1), (2,1),…

Q: Consider the equivalence relation on set A={a,b,c} given by R = {(a,a),(b,b),(c,c),(a,b),(b,c)} . s…

A:

Q: Without using the ?∞i=1 Ri representation of R+, Prove that for any set relation R (we did not pick…

A: Given: Let us consider the given, R+=∩Q:R⊆Q∧Q is transitive and prove that for any set relation R.

Q: Let Let A={2,4} and B = {1,3,5} and define relations U, V, and W from A to B as follows. For all (x,…

A: Given that -  Let A={2,4} and B = {1,3,5}

Q: Let A = {2, 3, 4} and B= {6, 8, 10} and define a relation R from A to B as follows: For all (x, y) ϵ…

A: Relation: A set is a ordered pair  is defined as a relation Let us consider the set A and B , then…

Q: Both P and Q are transitive relations on set X. Proof that a. Pn Q is also transitive b. PoQ is also…

A: Given,    Both P and Q are transitive relation on set X.

Q: Let R be the relation on the set S = {1,2, 3, a, b, c} given by xRy if and only if (x, y) E {(a, a),…

A: S=1,2,3,a,b,c To find: (a) , (b) , (c).

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: Define a relation S from R to R as follows:…

A:

Q: Find the number of relations from the set A {a, b, c} to the set B = {1,3}

A:

Q: Let A = {4, 5, 6} and B = {5, 6, 7} and define relations R, S, and T from A to B as follows: For all…

A:

Q: 9.13. Let S = {a, b, c}. Then R= {(a,b)} is a relation on S. Which of the properties reflexive,…

A:

Q: et A={1,2} and B={1,2,3} and define a relation R from A to B as follows: •Given any (x,y) element A…

A:

Q: For the set A = {are, bot, cab, era)}, define the relation R on A to be: (x,y) eR if and only if…

A: As per the condition, in every order pair there should be only 1 letter in common.

Q: 1. Consider the relation < on the set {1,2, 3, 4}. Write down this relation as a set of ordered…

A:

Q: See the instructions for Exercise (19) on page T00 from Section 3,1 (a) Proposition. Let R be a…

A: We use definition for following question

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: This question refers to unions and intersections of relations. Since relations are subsets of…

A: The given sets are: A={-2,2,3,5} and B={2,3}

Q: 1. Let A = {a, b, c} and B = {r,s, t, u}. Furthermore, let R = {(a, s), (a, t)}, (b, t) be a…

A: Suppose A and B are non empty sets. Define a relation R:A-&gt;B then, Domain of R={x: (x,y) belongs…

Q: How many relations are there on the set {a, b, c, d}

A: Introduction: The relation is a subset of the Cartesian product of two sets. Since it is a subset of…

Q: Our universe U is Z (integers), and R is the relation defined by R(x,y):=x<y^2 For example,  R(3,-2)…

A:

Q: This question refers to unions and intersections of relations. Since relations are subsets of…

A: A={-4,4,7,9}B={4,7} A×B=-4,4,-4,7,4,4,4,7,7,4,7,7,7,4,7,7,9,4,9,7

Q: 1. Consider the following relations defined on the set {a, b, c}. For each relation, determine…

A: (a) Reflexive functions are the ones whose domain and range are the same  for instance a,a∈R1 So…

Q: (1) Let A-(a,b,c,d), define a relation R on set A as follows: R-((a,a). (a,b), (b,a), (b,b), (c,c),…

A: Reflexive relation:  A relation R on set X is said to be reflexive if for all elements x∈X we have…

Q: Let A = { 2, 3, 4 } and B = { 4, 6, 8, 10 } and define a relation R from A to B as follows: %3D For…

A:

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: We defined the relation between sets by A - B means that there there is a 1-1 correspondence f : A →…

A: The complete solutions is in given below

Q: Let the relation R be {(1,2), (2,9), (5,6)}. Is R transitive? Give the reason.

A: Given : 1,2, 2,9, 5,6