4 Elephants and frogs, In this problem, A is the set of all animals, E is the set of all elephants and F is the set of all frogs, and is a relation on A defined by ab if and only if a can jump over b. Write in mathematical notation with quantifiers: "Any two frogs that can both jump over the same elephant can also jump over each other." Write in words: "Vxe A, (3ye E,yox) ⇒ x€ F." Explain in words what it would mean for to be transitive.

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…

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Q: Let T be an irreflexive relation on the set M, then the ToT relation is also irreflexive on the set…

A: Let M=ℕ. Define relation T on M as, T=a,b : a≠ b Clearly a,a∉T for any a∈M. Hence T is irreflexive.

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Q: Consider the following relation on set B = {a, b, {a}, {b}, {a, b}}: P = {(a, b), (b, {a, b}), ({a,…

A: Given that, The set B is: B=a, b, a, b, a, b And, the set P is: P=a, b, b, a, b, a, b, a, b, a, a, a

Q: A relationR on a set A is called equivalence if R is:

A: Equivalence Relation: A relation R on a set A is said to be an equivalence relation if and only if…

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A: We have been given a diagram for a relation R on a set A. To Do: We have to write the sets A and R.

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Q: Which of the following relations are transitive? The relations are in bold. (Remember: A relation R…

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Q: 7 Part 3 of 4 ! Required information NOTE: This is a multi-part question. Once an answer is…

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Q: Give an example of two equivalence relations R and S on

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Q: ame programs. A = the set of all people in the Social Security database; a Rb if and only if a and b…

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Q: S and T are binary relations on the set {a, b, c, d} and are defined as follows: S%3{ (а, b), (a,…

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Q: Which of the following does not denote a set?   a. N={x|x≥0} b. S c. {1,2,3} d. 2R3

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Q: 6. Let X and Y be subsets of {a,b}. Write the relation where X is related to Y if |X| = |Y| as a set…

A: Let  A={a ,b }  Cardinality of A=2 so the cardinality of power set is 2^2 =4 Now power set of A is…

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

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Q: A relation is an equivalence relation if it satisfies three properties. which of the following…

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Q: Let A and B be any two sets. A binary relation from A to B is i. CAXB ii. SANB CAUB Non of these…

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Q: x R y in R if | x |=||

A: we have to find the relation R where R is defined by x R y in ℝ if x=y, equivalent or not.

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Q: Question 4 Let S be a set such that |S| = 10. How many relations over S are there that are symmetric…

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Q: Let A be a set and R and S be relations on A. Dene the relation R + S on A by R + S = (R-S) […

A: 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) ∪…

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A: 6 Given set is A=1,2,3. Consider the relation R and S on A is given by  R=1,1,2,2,3,31,2,2,1 And…

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Q: (a) Let A = {a} and B = {1}. List all relations from A to B. (*Hint*) {a} and B = {1,2}. List all…

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Q: Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be…

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Q: If a set A has 5 elements, then the total number of possible relations on A is 255 252 25 52

A: Given below the detailed solution.

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Q: Let A De a set and ns Ol A. Che R+S = (R – S)U (S – R). Show that: (b) but R+S is countable. Show…

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