Let A be the set of all permutations of the 26 letters in the English alphabet. The relation R on A is defined by R = {(p, q) EAX A: the first letter of p precedes (in alphabetical order) the first letter of q} satisfies the anti-symmetric property. O True O False

Q: Determine whether the following statements are True or False: a - For all relations R and S, ROS=SOR…

A: We solve this using counter examples .

Q: Let W be the set of words in the English language. Define a relation R on W by W₁ R W₂W₁ and we have…

A: We are given that,      w1 R w2  <=> w1 and w2 have a letter in common.  Now, it is obvious…

Q: Let a1 = [-2  h], and a2 = [10  -20] The set {a1,a2} will span R3 unless h

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Q: Let S = (1, 2, 3, 4). With respect to the lexicographic order based on the usual less than relation,…

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Q: Define a relation R on the set N of natural numbers by R = {(x, y) : y = x + 5, x is a natural…

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Q: let R be the relation on the set of positive integers in which a R b if and only if a is a factor of…

A: Given below the detailed Solution.

Q: Let A:= {2} and B:= {2,3,5}. Give the Cartesian product of sets A and B, furthermore the power set P…

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Q: (2.3) Prove that R is an equivalence relation.

A: Prove R is an equivalnce relation.

Q: A. Let R be a relation on set A. A={x: xeJ and 0 sxs 12), and R-{(a,b) : la - b| is multiple of 6}.…

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: Let R and S be two relations both on A. Show that (a) If R and S are both reflexive, is RnS also…

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Q: Let A = {1, 2, 3, 4, 5} and R be the relation defined by R = {(1,1), (2,2), (2,4), (2,5),…

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Q: Let A = {1, 2, 3, 4, 5, 6, 7, 8}.  How many possible symmetric relations over A contain the ordered…

A: A relation R is said to be symmetric if a,b∈R implies b,a∈R. It is given that A = {1, 2, 3, 4, 5, 6,…

Q: Give an example of relation on {1,2,3,4} that is reflexive, not symmetric, and not transitive

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Q: How many relations are there on the set {a, b, c, d}

A: Introduction: The relation is a subset of the Cartesian product of two sets. Since it is a subset of…

Q: Let A = {1,2,3} and B = {1,2,3, 4}. The relations R1 = {(1,1), (2,2), (3,3)} and R2 = {(1,1), (1,2),…

A: Given that  R1={(1,1),(2,2),(3,3)}R2={(1,1),(1,2),(1,3),(1,4)} We need to find  a. R1∪R2b. R1∩R2c.…

Q: Let A={5,10,15,20, 25} and a partition of A be: {5,25},{10, 20} , {15} (a) Write all pairs of the…

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Q: prove why each relation has or does not have the properties: reflexive, symmetric, anti-symmetric,…

A: Step 1:   The given relation is defined as:

Q: List all the ordered pairs in the relation R= {(a, b) | gcd(a,b) = 1} on the set {2, 3, 4, 5, 6}.

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