Let S be a set with a finite number of elements, and let f: S - S be a map _ (a) If fis onto, can If f is 1-1, can f not be onto? Do your conclusions remain valid even if S has an infinite number f not be 1-1? (b) |(c) of elements?

Q: 6. Let S be a set and suppose is a relation on S. For each of the following, provide a…

A: Let us solve the given problems on relation in the next steps.

Q: Set A is bounded above if and only if set -A is bounded below.

A:

Q: Let f: A→B be a function. Prove or disprove the equivalence: (a) f is injective (b) If C is any set…

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Q: 1. Give an example of a set S with a relation ~ on S such that ~ is symmetric and transitive but not…

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Q: Suppose f function between infinite sets A and B, f is not onto function, does the sets A and B have…

A: Yes. It is possible that A and B have same cardinality. Let A and B both are the set of natural…

Q: Prove that for any set relation R (we did not pick it to be "on" any particular set) R* =N{Q:RC Q^ Q…

A: Given that any set relation R.

Q: 11.0, Prove that the interior of the interin of a set is equal to the interies of that set

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Q: . Is it true that the null set is a subset of every other set? (Y/N)

A: If a set has no element then the set is called null set. Null set is also called empty set. It is…

Q: |x²| = p^ n

A: Given: X=pWe need to show that Xn=pn

Q: Let f: X->Y and g:Y->X be maps between sets. Suppose that g ∘ f is equal to the identity map id_X:…

A: Given f:X→Y and g:Y→X be the maps between the sets.  Suppose that g∘f=idx. Then We need to prove or…

Q: Let F be a nonempty family of transitive relations. Prove that intersection F is a transitive…

A: Given F be a nonempty family of transitive relations. We have to prove that the intersection F is a…

Q: Let & = (A xEA) be a family of sets, and let B be a set, Then B- (UA) = U (B-A). «ΕΔ a EA True False

A:

Q: 5.6.34. (a) Find an example of set A and a nonempty subset B C A, such that A and A \ B have the…

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Q: Let B be a denumerable set and let A be a non-empty set of unspecified cardinality. If f : A --> B…

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Q: 3) Let X be a set with > 3 elements. Show that there exist bijective functions f :X → X and g : X +…

A: Let x=1,2,3 then, f=123132g=123321 `

Q: Consider the Datalog programs P1 (left) and P2 (right) below, which use relations R(A, B) and S(A,…

A: Option (B) is correct because T3 and T4 include same set of tuples

Q: Let R be a relation on A. Then for all n ≥ 0, prove R^n is a set. (Discrete Mathematics, powers of a…

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Q: 7. A relation R on a set X is called an equivalence relation if it is symmetric, reflexive, and…

A: Equivalence relation: A relation R on a set X is called an equivalence relation if it is symmetric,…

Q: 3. ** Let X, Y be finite sets, and f is a function XY. What can you say about the cardinality if X,…

A: 3. Given X, Y are finite sets and f:X→Y is a function   To Comment about cardinality of X and Y if…

Q: 5. Let~ be an equivalence relation on a set S. We define f: S→S/~ f(x) = [a], where a € S such that…

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Q: (Chapter 11.4, #3) The relation relation. Sketch it, by drawing Z as a subset of the line, then…

A: The objective is to show that x≡ymod4 is an equivalence relation. To show the relation is an…

Q: 5. Let X be the set X = {1,2,3}, and let R be the relation defined on X by x₁ Rx₂ if x1 + x2 3. (a)…

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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: If f:{1,2,3}->{a,b}, f(1)=a f(2)=b f(3)=a then explain why f is onto but not one to one

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Q: Find an orthogonal set with the same span (and same number of elements) as [2] [8]} (18118)} "

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Q: 3.) Nowe consider motrix cif possible) as a linear combination of the motrices in' ls. the set s…

A: Given that: S=3-333,3-245,6-3106To express the the following matrices in the linear combination of…