Let A = {0, 1, 2} and let S be the set of all strings over A. Define a relation L from S to Znonneg follows: For every string s in S and every nonnega- tive integer n, as (s, n) E L means that the length of s is n. Then L is a function because every string in S has one and only one length. Find L(0201) and L(12).

Q: 35. For each real number x, let f(x)=x². For any two real numbers a and b, define a -b provided that…

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Q: Determine the following for the given relation R on the set { 1, 2, 3, 4, 5, 6 } defined by the rule…

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Q: Let A={3,4,6,7}, and define a relation R on A as follows: For every x, y belong to A, xR y x|y.…

A: We first write elements of R then we form diagraph and then we write the corresponding adjacency…

Q: Let A = {1,2,3,4} and B = {5, 6, 7}. Let f be the relation f = {(1,5). (2,5), (3,6), (?, ?)} where…

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Q: 3. Let a, b, c, d be real numbers with a < b and c < d. Find a one-to-one correspondence between (a,…

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Q: Let  X = {a, b, c}  and  Y = {d, e, f, g}.   Define functions H and K by the arrow diagrams below.…

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Q: Let A and B be two nonempty sets, f: A → B be a function and R be an equivalence relation on the set…

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Q: 2,3,4,5

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Q: Let A = {1,2,3,4} and B = {5, 6, 7). Let f be the relation f = {(1,5), (2,5), (3, 6), (?, ?)} where…

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Q: Given a relation g from the set D = {1, 2, 3, 4, 5} to the set C = {a, b, c, d}, where g = {(1, a),…

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Q: {2, 4, 6, 8} and define a relation R from A to Bas follows: for all (x,y) E AX B, (x, y) ER T. set…

A: As per our guidelines we are supposed answer only 3 subparts and rest can be reposted Given Data:…

Q: Let A = {1, 2, 3) and B = {4, 9, 21, 25). Define the relation R from A to B by a R b if a divides b.…

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Q: Let A be the set of all strings of 0's, l's, and 2's of length 4. Define a relation R on A as…

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Q: Consider the set M = {0, 2, 4, 6} and N = {1, 3, 5, 7}. Determine if each of the following ordered…

A: According to guideline we need to solve first 3 subparts.

Q: Let Y = {0,1,2} and Z = {0,1} and define a relation R from Z to Y as follows: Given {x, y} € Z x Y,…

A: Relation : A relation between two sets is a collection of ordered pairs containing one object from…

Q: Let S be the set of ordered pairs of positive integers, and define (a,b) R (c,d) to mean that 2a-d =…

A: A relation R is transitive on a set A if xRy and yRz then xRz for all x,y and z belong to A. Now,…

Q: 9. Let R+ denote the set of positive real numbers. Define a relation E on R+ as follows: a Eb if and…

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Q: Let A = {0, 1, 2} and B = {0, 8, 9}. If R is the relation from A to B such that (a, b) ∈ R provided…

A: If ab=0 then either a or b is equal to 0 Both also can be 0.

Q: Let A = {3, 5, 7, 8} and define a relation S from A to A as follows: %3D For all (x, y) E A × A, (x,…

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Q: A = {1, 3} and B = {2, 4, 6}. Define a relation R from A to B as follows: for all (x, y) ∈ A × B…

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Q: Let A = {3, 5, 7, 8} and define a relation S from A to A as follows: For all (x,y)∈A×A,(x,y) ∈ S if…

A: Solution : Given :             A = {3, 5, 7, 8} ,                         S is a relation from A to…

Q: (b) Observe that all the relations in (a) are equivalence relations. Prove that this is true in…

A: Given: A is a nonempty set, and P is a partition of A. To show: The relation R is equivalence…

Q: A relation R is defined on the A={1,2,3...9.10}  as follows: xRy means "3x- 2y=1"   List the…

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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: Let A = {1,2, 3, 6}. Define a relation R on A as follows: x Ry if y – x > 0 Write out the relation R…

A: We have to find the relation and write as set notation.

Q: 8. Let A = {1,2} and B = {a, b, c}. For each of the following cases, decide whether the set…

A: The set A={1,2}, B=a,b,c &amp; f:A→B. a) 1,a,2,b b) 1,b,2,b c) 1,a,1,b,2,c

Q: Let A = {2, 3, 4, 5} and B = {6, 8, 10}. A relation R is defined from A to B by a R b if a | b and…

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Q: Let R be a relation on Z given by aRb if and only if a = b². Is this relation a function? Justify…

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Q: Given a relation g from the set D = {1, 2, 3, 4} to the set C = {a, b, c, d} where g= {(1, a), (2,…

A: A relation  from the set  to the set  where .The objective is to determine whether the relation is a…

Q: 5. Let A = {6, 8, 10, 15, 17} and B = {2, 3, 4, 5} and define a relation R: A → B as follows: For…

A: Given: A={6, 8, 10, 15, 17} B={2, 3, 4, 5} Relation R:A→B is: For all x,y∈A×B∈R if and only if…

Q: 3. (ey + 1)²e-dx + (ex + 1)³e¯*dy = 0

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Q: For the set A = {are, bot, cab, era)}, define the relation R on A to be: (x,y) eR if and only if…

A: As per the condition, in every order pair there should be only 1 letter in common.