Let A = {0, 1, 2, 3} and define relations R, S, and T on A as follows: R = {(0, 0), (0, 1), (0, 3), (1, 0), (1, 1), (2, 2), (3, 0), (3, 3)}, S = {(0, 0), (0, 2), (0, 3), (2, 3)}, T = {(0, 1), (2, 3)}. a. Is R reflexive? symmetric? transitive? b. Is S reflexive? symmetric? transitive? c. Is T reflexive? symmetric? transitive?

Q: Consider the relation R = {(1, 2),(2, 1),(2, 3),(3, 4),(4, 1)} on {1, 2, 3, 4}. Is R transitive?…

A: Answer : No , the above relation is not transitive .

Q: إجابتك PWhich of these relations on {0, 1, 2, 3} are equivalence relations a) {(0, 0), (1, 1), (2,…

A: The correct answer of the questions is Option ("a")" { (0, 0) (1, 2) (2, 2) (3, 3) }"

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A: Handwritten Solution of all the parts given below:

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A: Here is the solution which is mentioned below:

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A:

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A:

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Q: 3.7 Consider a fuzzy relation RC A × A where A = {a, b, c}. R a b d e a 1 1 1 1 1 1 d. 1 1 1 1 a)…

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Q: Show that the following decomposition of the schema R of Exercise 7.1 is not alossless…

A:

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A:

Q: Suppose a relation schema R = (A, B, C, D) is decomposed into following relations R1(A,B,C) and…

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A: Given:

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A: This is of discrete mathematics

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A:

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A: I have provided solution in step2

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A: Below i have answered 1 st question only:

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A: using Armstrong's axioms=&gt; proved in figure figure 1:

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A: Answer :-)

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A: I Have answered this question in step 2.

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Q: If R is a relation on I such that xRy if and only if x<y, then R is a partial order relation.

A:

Q: If R is a relation on I such that xRy if and only if x<y, then R is a partial order relation.

A: NOTE: This question is related to data structure and Discrete mathematics and very useful in mapping…

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A: The Answer is

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A: Answer: The correct option is “(d) All of them”

Q: Let the following be premises: * C- A * - A * -C - - B - Dv B

A: Given premises:   C→A¬ A¬ C→ ¬ B¬ D∨B

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A: Consider the given diagram :