Suppose D, R are sets of sizes |D| = d, |R| = r. How many functions f : D → R are there if . (a) ...
Suppose D, R are sets of sizes |D| = d, |R| = r. How many functions f : D → R are there if .
(a) there are no further restrictions?
(b) r ≥ d and f must be injective?
(c) r = d and f must be a bijection?
(d) d ≥ r = 2 and f must be surjective?
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Suppose D, R are sets of sizes |D| = d, |R| = r. How many functions f : D → R are there if . (a) ...
Suppose D, R are sets of sizes ID-d, R-r. How many functions f : D → R are there if … (a) ...ther...
Please provide an explanation for each part of the question.
Thanks!
Suppose D, R are sets of sizes ID-d, R-r. How many functions f : D → R are there if … (a) ...there are no further restrictions? r d and f must be injective? (c) ...r- d and f must be a bijection? (d) ..d2r2 and f must be surjective?
Suppose D, R are sets of sizes ID-d, R-r. How many functions f : D → R are there...
Let f : A rightarrow D and g : B rightarrow C be functions. For each...
Let f : A rightarrow D and g : B rightarrow C be functions. For each part, if the answer is yes, then prove it, otherwise give a counterexample. Suppose f is one-to-one (injective) and g is onto (surjective). Is go f one-to-one (injective)? Suppose f is one-to-one (injective) and g is onto (surjective). Is g f onto (surjective)? Suppose g is one-to one. Is g one-to-one? Suppose g f onto. Is g onto?
A. (Leftovers from the Proof of the Pigeonhole Principle). As before, let A and B be finite sets with A! 〉 BI 〉 0 and let f : A → B be any function Given a A. let C-A-Va) and let D-B-{ f(a)} PaRT...
A. (Leftovers from the Proof of the Pigeonhole Principle). As before, let A and B be finite sets with A! 〉 BI 〉 0 and let f : A → B be any function Given a A. let C-A-Va) and let D-B-{ f(a)} PaRT A1. Define g: C -> D by f(x)-g(x). Briefly, if g is not injective, then explain why f is not injective either. Let j : B → { 1, 2, 3, . . . , BI}...
Let R represent the set of all real numbers. Suppose f:R -> R has the rule...
Let R represent the set of all real numbers. Suppose f:R -> R has the rule f(x)=3x+2. Determine whether f is injective, surjective and/or bijective. Injective but not Surjective Surjective but not Injective Bijective (both Injective and Surjective) None of the above
(1 point) Suppose f, g: R² + R2 are continuous functions, where g is surjective. Determine...
(1 point) Suppose f, g: R² + R2 are continuous functions, where g is surjective. Determine if the following sets are open, closed, neither, both or if it can't be determined. 1.9-1 (R) 2. (f • g)-+ ({(1, 2)}) 3. (f+9) (B(0; 1)) 4. (f+g)-1({(x, y) : x > 0}) 5.9-1 (B(0; 1))
Show your work, please 7. Functions. Is the following function from R to R injective and/or...
Show your work, please
7. Functions. Is the following function from R to R injective and/or surjective? Prove your answer. If bijective, find the inverse function. f(x) = 2.c 1 + x2
Show your work, please 7. Functions. Is the following function from R to R injective and/or...
Show your work, please
7. Functions. Is the following function from R to R injective and/or surjective? Prove your answer. If bijective, find the inverse function. f(x) = 2.c 1 + x2
5. Let A = P(R). Define f : R → A by the formula f(x) =...
5. Let A = P(R). Define f : R → A by the formula f(x) = {y E RIy2 < x). (a) Find f(2). (b) Is f injective, surjective, both (bijective), or neither? Z given by f(u)n+l, ifn is even n - 3, if n is odd 6. Consider the function f : Z → Z given by f(n) = (a) Is f injective? Prove your answer. (b) Is f surjective? Prove your answer
Ty Are the two statements logically equivalent? Why or why not? Let f:{a,b,c} - {1,2,3} (a)...
Ty Are the two statements logically equivalent? Why or why not? Let f:{a,b,c} - {1,2,3} (a) How many such functions are there? (b) How many are injective, how many are surjective, and how many are bijective
Question4 please (1). Let f: Z → Z be given by f(x) = x2. Find F-1(D)...
Question4 please
(1). Let f: Z → Z be given by f(x) = x2. Find F-1(D) where (a) D = {2,4,6,8, 10, 12, 14, 16}. (b) D={-9, -4,0, 16, 25}. (c) D is the set of prime numbers. (d) D = {2k|k Ew} (So D is the set of non-negative integer powers of 2). (2). Suppose that A and B are sets, C is a proper subset of A and F: A + B is a 1-1 function. Show that...
Please provide an explanation for each part of the question.
Thanks!
Suppose D, R are sets of sizes ID-d, R-r. How many functions f : D → R are there if … (a) ...there are no further restrictions? r d and f must be injective? (c) ...r- d and f must be a bijection? (d) ..d2r2 and f must be surjective?
Suppose D, R are sets of sizes ID-d, R-r. How many functions f : D → R are there...
Let f : A rightarrow D and g : B rightarrow C be functions. For each part, if the answer is yes, then prove it, otherwise give a counterexample. Suppose f is one-to-one (injective) and g is onto (surjective). Is go f one-to-one (injective)? Suppose f is one-to-one (injective) and g is onto (surjective). Is g f onto (surjective)? Suppose g is one-to one. Is g one-to-one? Suppose g f onto. Is g onto?
A. (Leftovers from the Proof of the Pigeonhole Principle). As before, let A and B be finite sets with A! 〉 BI 〉 0 and let f : A → B be any function Given a A. let C-A-Va) and let D-B-{ f(a)} PaRT A1. Define g: C -> D by f(x)-g(x). Briefly, if g is not injective, then explain why f is not injective either. Let j : B → { 1, 2, 3, . . . , BI}...
Let R represent the set of all real numbers. Suppose f:R -> R has the rule f(x)=3x+2. Determine whether f is injective, surjective and/or bijective. Injective but not Surjective Surjective but not Injective Bijective (both Injective and Surjective) None of the above
(1 point) Suppose f, g: R² + R2 are continuous functions, where g is surjective. Determine if the following sets are open, closed, neither, both or if it can't be determined. 1.9-1 (R) 2. (f • g)-+ ({(1, 2)}) 3. (f+9) (B(0; 1)) 4. (f+g)-1({(x, y) : x > 0}) 5.9-1 (B(0; 1))
Show your work, please
7. Functions. Is the following function from R to R injective and/or surjective? Prove your answer. If bijective, find the inverse function. f(x) = 2.c 1 + x2
Show your work, please
7. Functions. Is the following function from R to R injective and/or surjective? Prove your answer. If bijective, find the inverse function. f(x) = 2.c 1 + x2
5. Let A = P(R). Define f : R → A by the formula f(x) = {y E RIy2 < x). (a) Find f(2). (b) Is f injective, surjective, both (bijective), or neither? Z given by f(u)n+l, ifn is even n - 3, if n is odd 6. Consider the function f : Z → Z given by f(n) = (a) Is f injective? Prove your answer. (b) Is f surjective? Prove your answer
Ty Are the two statements logically equivalent? Why or why not? Let f:{a,b,c} - {1,2,3} (a) How many such functions are there? (b) How many are injective, how many are surjective, and how many are bijective
Question4 please
(1). Let f: Z → Z be given by f(x) = x2. Find F-1(D) where (a) D = {2,4,6,8, 10, 12, 14, 16}. (b) D={-9, -4,0, 16, 25}. (c) D is the set of prime numbers. (d) D = {2k|k Ew} (So D is the set of non-negative integer powers of 2). (2). Suppose that A and B are sets, C is a proper subset of A and F: A + B is a 1-1 function. Show that...
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