R and S are relations on set A = {1,2,3,4}, defined as R = {(1,2},(1,3),(2,3),(2,4),(3,1)}; S = {(2,1},(3,1),(3,2),(4,2)}. Find S o R, R o S, R-1, S-1,where o means composition.

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 A be the towns {P, Q, R, S}. Let B be the one way street relation {(P, S), (Q, P), (R, P), (S,…

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Q: Let A={3,6,9}, B={2,4,6,8}, C={ 1,2,3,4,5}and the universal set U={0,1,2,.,10}. Find each set (a)…

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Q: true or false and why ? The set [0,1] has the same cardinality as ℝ .

A: True. See the attachment

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: Let U=(3,4,8,9,10,11,15,18,19), X=(4,9,11,18), Y = {4,8,9,10,11), and Z=(3,4,8,18,19). List the…

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Q: What are the equivalence classes of the equivalence relations on {0, 1, 2, 3}?

A: Answer:-  Find the equivalence classes of the equivalence relations on A = {0, 1, 2, 3}?

Q: How many relations are there on the set S = {2, 4, 6}?

A: We know that, the number of relations of a set containing n element is 2n^2. Given that S = {2,4,6}

Q: |Given the relation R= {(1,1), (2, 4), (3, 1), (4, 1), (5,2)} on the set A= {1,2,3,4,5), find the…

A: We know: Symmetric closure of a relation R, △, is obtained by adding (b, a) to R for each (a, b) ∈ R…

Q: 1. Consider the following relations on the set A = {1,2, 3, 4}. = {(1, 1), (1,3), (1, 4), (2, 2),…

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Q: Suppose p and o are relations defined on S = {1, 2, 3, 4} by the sets p = {(2, 2), (3, 2), (3, 4),…

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Q: Which of the following is an equevalence relation on the set (a, b, c} 7 O (a, a), (a, b), (b, a).…

A: Option 1 is equivalence relation. Option 2 is also is an equivalence relation. Option 3 and 4 is not…

Q: Theorem 2. Let R and S be binary relations on a set X. Then, (a) (R-1)-1 = R. (b) (RUS)-1 = R-'Us-!.…

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Q: There are 6 towns {A, B, C, D, E, F} with the following one way street relation {(A, B), (A, C), (B,…

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Q: Obtain the 16 relations of the set {0,1}, indicate which of these are reflexive, symmetric and / or…

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Q: Let R1, R2, R3 be relations on { a, b, c, d, e }. Find the transitive closures, given their…

A: i) R1 = { (a, c),(b, d),(c, a),(d, b),(e, d) } To find the transitive closure of R1, we need to find…