By listing the elements as ordered pairs, define a relation on the set A = {e, 2, 7, ♡} which is: (a) not reflexive, not symmetric, and not transitive; (b) reflexive, symmetric, and transitive; (c) reflexive, not symmetric, and transitive; (d) reflexive, symmetric, and not transitive.

Q: Let A = {a, b, c} Define a relation as follows: ARA = {(a, b) , (a, c) , (b, c)} To obtain the…

A: Transitive relation means if (x, y) and (y, z) are in R, then (x, z) will also be in R.    Using…

Q: For each relation, indicate whether the relation is: • Reflexive, anti-reflexive, or neither •…

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Q: On the set A = {a, b, c, d, e, f, g, h} is given by the relation R = {(a; b), (a; c), (a; d), (a;…

A: The set is A=a, b, c, d, e, f, g, h and the relation is R=a; b, a; c, a; d, a; e, b; f, c; f, d; g,…

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

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Q: Consider the relation R = {(a, b) | a divides b} on the set {1, 2, 3, 4, 5, 6}. i. List all the…

A: The given relation is         R={(a,b)| a divides b} so to find the ordered pairs in the relation R,…

Q: Let A = {1, 2, 3, 4}. Give an example of a relation on A that is:    (a) reflexive and symmetric,…

A: Let A=1,2,3,4. To give an example of a relation on A that is:  (a) reflexive and symmetric, but not…

Q: Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9} and let R be the relation {(a,b) ! a , b} Find the smallest…

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Q: Select all pairs in the reflexive closure of the relation R, defined on the set A = { a, b, c, d }…

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Q: Let A = {4, 5, 6} and B = {6, 7, 8} and let S be the "divides" relation from A to B. That is, for…

A: Here given sets A = {4, 5, 6} and B = {6, 7, 8} and relation defined asxSy⇒x/y means x, y∈S⇒x…

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

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Q: Let A= {0,1,2,3,4} and a partition of A be: {0,2},{1},{3,4} (a) Write all pairs of the relation…

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Q: Decide whether each of the following relations is an equivalence relation or not.  {(a, b) | gpa of…

A: To prove equivalence relation, we have to prove that (i) the relation is reflexive, (ii) the…

Q: Could you please help me?

A: The example of the set and their relation which is Symmetry , Transitive but not reflexive  A=1,2,3…

Q: Let R be the relation, {(a, b) e N x N:a + b is odd}. Give an example that shows that R is not…

A: Given R be the relation, {(a, b) ∈ N x N:a + b is odd}.  We find an example that shows that R is not…

Q: For the relation, indicate whether the relation is: • Reflexive, anti-reflexive, or neither •…

A: A relation R defined on a set S is said to be Reflexive if xRx for all x in S.  Anti reflexive  if…

Q: Let R be a relation from A to B and defined "x is at least twice as big as y." Write R as a set of…

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Q: For each relation on {0, 1, 2, 3} below show that the relation is an equivalence relation, or show…

A: I have used the definition of equivalence relation

Q: True/False: The relation R = {(a, a), (a, b), (b, a), (b, b), (c, c), (a, c), (b, c), (c, b), (d,…

A: The given set is                         S = { a , b , c , d }  and the given relation is…

Q: Given the digraph below of a relation R on A = (a,b,c,d), write all the ordered pairs that are in R.

A: We are required to find all the ordered pairs that are in R from the diagraph given in the question.…