A relation R on a set A is defined to be irreflexive if, and only if, for every  x ∈ A,  x R x; asymmetric if, and only if, for every  x, y ∈ A  if  x R y  then y R x; intransitive if, and only if, for every  x, y,   z ∈ A,  if  x R y  and  y R z  then x R z. Let  A = {0, 1, 2, 3},  and define a relation  R4  on A as follows. R4 = (1, 2), (2, 1), (1, 3), (3, 1) Is  R4  irreflexive, asymmetric, intransitive, or none of these? R4 is irreflexive.R4 is asymmetric.R4 is intransitive.R4 is neither irreflexive, asymmetric, nor intransitive.

Q: If A = {1,2,3,4} give an example of a relation R on A that is: Reflexive and symmetric but not…

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Q: 1. If f is a function on a set A = {1,2,3,4,5} such that f = {(1,2), (2,3), (3,4), (4, x), (5,5)}.…

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Q: a)Let R be a relation on the set Z × Z defined by the following rule: For all (a, b),(c, d) ∈ Z × Z,…

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Q: Is the following statement true or false? If R is any symmetric relation on a set A, then R is…

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Q: 2. Let D be a relation defined on Z as follows: For all x, y € Z, x D y iffx|y. Determine if D is…

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Q: 2,3,4,5

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Q: Let A={a,b,c,d,e}. Find a relation R on A which is symmetric and transitive but not reflexive

A: Reflexive relation means every term of a set is related with itself

Q: 1. Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9}. Let P = P(A) be the power set of A. Let R be the relation on…

A: (a) For any X ∈ P,            | X ∪ X | = |X|           | X ∪ {1, 2} | = |X| + |{1, 2}| - |X ∩ {1,…

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: Let A ={1, 2}, B = {1, 2, 3} define a relation R from A to B given any {x, y} ϵ A cross B.…

A: A=1, 2, B=1, 2, 3 R is a relation defined as R=x, y: x+y2 is an integer.

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

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Q: Let A be a set and R and S be relations on A. Define the relation R+S on A by R+S = (R – S)U(S – R).…

A: Given A be a set and R and S be relations on A. R+S on A is defined by R+S=R-S∪S-R=R∪S-R∩S=R∪S∩R∩Sc…

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Q: (i) Let A = {1,2,3,4,5), then either find a relation on A that is not reflexive on A and not…

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Q: A = {1, 3} and B = {2, 4, 6}. Define a relation R from A to B as follows: for all (x, y) ∈ A × B…

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Q: Let A = {3, 5, 7, 8} and define a relation S from A to A as follows: For all (x,y)∈A×A,(x,y) ∈ S if…

A: Solution : Given :             A = {3, 5, 7, 8} ,                         S is a relation from A to…

Q: 1. Define a relation R on R? by stating that (a, b)R(c, d) if and only if a? + b <c? +d². Show that…

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Q: (a) x and y are in the same major. (b) x and y have the same last name. (c) x and y are taking a…

A: See the attachment

Q: set {(a,b),(a, a), (c, a), (b, b)} (a). Let X = {a,b,c} be sets. is a relation on X and find its…

A: Answer and explanation is given below..

Q: A relation R on a set S is said to be transitive ifffor all x, y, z ∈R, xRy ∧ yRz ⇒ xRz. Relation R…

A: It is given that A relation R on a set S is said to be transitive ifffor all x, y, z ∈R, xRy ∧ yRz ⇒…

Q: Let Let R be a relation from A to B defined by Then Select one: O a. O b. O d. A = {0, 1, 2, 3, 4}…

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Q: 1. Let R be a relation on the set A = {1, 2, 3, 4, 5, 6, 7} defined by R = {(a, b) ∈ A × A | 4…

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Q: Let A = {1, 2} and let B = {2, 4, 7}. Let R be a relation defined as follows: (x, y) = R means that…

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Q: Suppose that R is a symmetric relation. Match the correct term with each blank space in the…

A: Suppose  that R is a symmetric relation than prove that R-1⊆R Proof: Suppose that &lt;x,y&gt;∈R-1.…

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Q: Let A = {1, 2, 3, 4}. Give an example of a relation on A that is (R = Reflexive, S = Symmetric, T =…

A: (a) Consider the Relation          V = {(1, 1), (2, 2), (3, 3), (4, 4), (1, 2), (2, 1), (2, 3), (3,…

Q: 5. Let X be the set X = {1,2,3}, and let R be the relation defined on X by x₁ Rx₂ if x1 + x2 3. (a)…

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Q: Reflexive. • Anti-reflexive. • Symmetric. • Anti-symmetric. Justify all your answers. Transitive. •…

A: Let's consider a few examples of elements inside the relation R, where (a,b)∈ R if and only if…

Q: Lex 172,3,4). Consider the relation R on X defined as follows. R = ((1.1), 13), (2,2), (2.4), (3,1),…

A: I have solved both subpart using basic definition of equivalence relation and equivalence class.

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