5. (a) How many functions are there from a set with n elements to a set with m elements?

Q: 7. i) How many functions are there from the set {1, 2, 3, ...,k} where k is a positive integer, to…

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Q: For what values of k will the set of ordered pairs ((1,10),(2,9),(3,8),(4,7),(k+2,6)} represent a…

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Q: For what values of n will the set {(1,3),(2,5),(n-1,1),(n,7),(n+ 1,0) represent a function?

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Q: How many one-to-one functions are there from a set with m elements to a set with n elements, where…

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Q: 13. Which of the following sets is a function? А. ((3, 1), (3, 2), (3,5)} B. {(-1,–1), (–2, 7),…

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Q: How many different functions are there from a set with 10 elements to sets with 2 elements?

A: Definition 1.Function : A relation where every input has one single output. 2.Product rule: If one…

Q: A.How many functions are there from set A with 4 elements to set B with 6 elements? B.How many…

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Q: For which values of k is the set of order pairs (2,4),(k,6),(4,0) a function?

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Q: . (Multiple Choice Question) The domain of the function x2 is the set: 4 - A) [1,2) U (2, 0) в) (2,…

A: 2x-1x2-4

Q: How many one-to-one functions are there from a set with three elements to a set with eight elements?

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Q: at is the domain of the relation below? All real numbers greater than or equal to 0. All real…

A: The domain of a function f(x) is the set of all values for which the function is defined, and the…

Q: Given the function f = {(1, 2), (2, 3), (3, 4)} write the set of ordered pairs representing f".

A: The given function:                     f=1, 2, 2, 3, 3, 4 The inverse of the function uses the…

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. Let A = {1,2, 3, 4}. Let F be the set of all functions from A to A. (a) How many pairs (f, 9) €Fx…

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Q: 2. What is the domain of the function x)- dx+6 in set notation? a. xS-6 b. x2-6 C. x20 d. xS0

A: Domain of the given function is given by

Q: . Let f= {(-4,4), (-2, 4), (1, 3), (3, 5), (4, 6)} and g= {(-4, 2), (-2, 1), (0, 2), (1, 2), (2, 2),…

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Q: what is the maximum number of functions one can make from a set of n elements to a set of m elements

A: If |A|=n  And  |B|=m  Then the number of possible function from A to B is m^n.

Q: Which of the following is a function one-one from the set A = {1,2,3} to B = {4,5,6} is: (Explain)…

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Q: 4. Which of the following set represents functions? * O A=((2,5),(1,0),(3,1),((4,2)}…

A: We first find which of the the given set represents a function.

Q: Let A= {a,b,c,d,q,z} and B= {1,2,…,10} and define the function (D) how many functions are there from…

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Q: 3. Let A = {(7,9), (8, 11), (11, 4), (4, 3), (1, 11), (13, 5), (17, 11)}. %3D a) Is A a function? b)…

A: We can answer all the subparts as below

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.