Consider functions f: {1,2,3,4)→ {a,b,c). a. How many functions are there? b. How many functions are injective? c. How many functions are surjective?

Q: Let A, B, C denote sets. Let g, h : A → B and f : B → C denote functions. Assume f is one-to-one and…

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Q: Consider sets A and B with |A| = 7 and |B| = 4. How many functions f: A → B are surjective?

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Q: 0 1 2 У 17 13 9

A: Given Table x y 0 17 1 13 2 9 3 5 4 1 5 -3

Q: What kind of functions is the function shown in this figure? b) odd e) Neither odd nor even d) None…

A: Consider the provided graph, A function f(x) is even if the graph of f(x) is symmetric with respect…

Q: Consider a ruler that takes as input any integer z and outputs. Is r a function? Why?

A: Given that r takes input as integer z and outputs Here the input is different while the output is…

Q: Does every one-to-one function has Select one: A. Both A and B B. same number of elements in…

A: In one to one function there is only one y value corresponds t the x value. The elements in the…

Q: 4. Lėt f:A total injective function. B and g: B→C be two functions. If gof is a bijective function,…

A: we know that  gof is Bijective,  hence, gof has one to one correspondence,  This deduces that g must…

Q: Let f, g be two functions from a set A to itself. If f o g is surjective, does it imply that g o f…

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Q: consider set a and b with |A| = 9 and |A| = 20 a. how many functions f : A -> B are there b. how…

A: Given set A and set B with A=9 and B=20 (a) We have to find the number of functions f:A→B. The…

Q: b) Let the set A = {-1,0, 1} and consider the following function: f2 A → A given by f₂(x) = (-x)4.…

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Q: Which term best describes the mapping shown? a. relation b. function c. one to one function

A: Given query is to find mapping is a relation or function.

Q: Consider sets A and B with |A| = 14 and |B| = 19. a. How many functions f : A → B are there? b. How…

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Q: Let f : A →B and g : B →C denote functions, and assume g ◦f is injective. a. Prove or disprove: The…

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Q: Q1. Let f: X-Y and g: Y - Z be two functions then a. If gof: X-Z bijective function then / and g are…

A: Step 1: Step 2: Step 3: Step 4:

Q: Let A = {1,2,...,n} and consider the functions f: A → A. a. How many functions satisfy f(1) = 1? b.…

A: This question related to function and bijection.

Q: Let a, b, c, d be numbers and f(x,y) be any function. Then . f(x, y) dxdy This statement is --- --…

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Q: Say whether the following function is injective, surjective, bijective, or none of the above (note:…

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Q: Let f: A -> B and g: B -> C be two functions. Prove: if f and g are surjective, then gof is…

A: Given: Let  f: A→B and g: B→C be two functions.  If f and g are Surjective(onto), To Prove:  g∘f:…

Q: A. Describe the error in the following: a. 5 is a subset of N b. x>1 and x 1<4 c. Given the function…

A: A. a. ) 5 is not a subset of N, its an element of N. It should be written as {5} is a subset of N.…

Q: ?: R2 → R, ?(?1, ?2) = ?1-?2 function is given. a) Can ? be an surjective function? b) Can ? be an…

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Q: Let f: A → B be a function, and let C be any set such that BCC. True or False: f : A → C is always a…

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Q: 1. Consider the functions f : A → B and g : B → C. a. If f and g are both injective, show that so is…

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Q: C = {4x + 1] x € Z+}, D = {c + d]c € C, d € C}, E = C × D Is C a subset of D or E? Explain a…

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Q: c) Let f: A B and g: B → C be surjective functions. Prove or disprove whether gof is surjective.

A: See the attachment

Q: What is the best description of the relation? -4 7- 11 10< 17 13 20

A: According to the definition of function: For a relation from x to y to be a function, every element…

Q: let A be a set with n elements and B a set with m elements. How many different functions are there…

A: Concept introduction: Relation: A relation between two sets is a collection of ordered pairs…

Q: 3. Construct table and sketch the graph of the function.f:x → 3x²,x €R for given domain x = -4,…

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Q: Consider sets A and B with |A| = 12 and |B|| 8. How many functions f : A → B are surjective?

A: We will find out the required value.

Q: Consider the set N²= NX N, the set of all ordered pairs (a, b) where a and b are natural numbers.…

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Q: Which of the following relations is not a function? a) b) V c) d)

A: To check whether the graph of a given relation is a function or not,we draw vertical lines which are…