Let A be a set with m elements and B a set of n elements, where...

Question

Question

Let A be a set with m elements and B a set of n elements, where m, n are positive integers. Find the number of one-to-one functions from A to B.

Answer 1

Answer #1

Given, A be a B be a set with set with m elements (men) also an elements (NEN) Here two possibility arise case 18 sein then t

Answer 2

Similar Homework Help Questions

Let A be a set with m elements and B be a set with n elements...

Let A be a set with m elements and B be a set with n elements in it. -When is it possible to have a k-to-1 function f such that f : A → B? -Count the number of k-to-1 functions f such that f : A → B
1. Suppose N is a set with n elements and M is a set with m...

1. Suppose N is a set with n elements and M is a set with m elements. a. If n <m, how many one-to-one functions are there from N to M? b. If n > m, how many onto functions are there from N to M?
1. (9pts) Suppose A is a set with m elements and B is a set with...

1. (9pts) Suppose A is a set with m elements and B is a set with n elements. a. How many relations are there from A to B? Explain b. How many functions are there from A to B? Explain C. How many relations from A to itself are reflexive? Explain

1. Let U be the universal set with disjoint subsets A and B, where n(U-46, n(A-15,...

1. Let U be the universal set with disjoint subsets A and B, where n(U-46, n(A-15, and n(B-14. Find nAn B 2. A merchant surveyed 300 people to determine the way they leaned about an upcoming sale. The survey showed that 180 learned about the sale from the radio, 170 from television, 130 from the newspaper, 120 from radio and television, 70 from radio and newspapers, 80 from television and newspapers, and 60 from all three sources. How many people...
QUESTION 19 Let P(m, n) be the statement "m divides n", where the domain for both...

QUESTION 19 Let P(m, n) be the statement "m divides n", where the domain for both variables consists of all positive integers. (By “m divides n” we mean that n = km for some integer k.). is an Vm P(m,n). O a. False b. "False" and "not a tautology" O c. True d. Not a tautology QUESTION 23 Let P(m, n) be the statement "m divides n", where the domain for both variables consists of all positive integers. (By “m...
5. Suppose P(m,n) means “m>n”, where the universe of discourse for m and n is the...

5. Suppose P(m,n) means “m>n”, where the universe of discourse for m and n is the set of POSITIVE integers. Find the truth value of each statement and explain your answer. NOTE: This is NOT exactly the same as the practice test. (a) (2 points) VxP(x,5) (b) (2 points) Vx3yP(x,y) (c) (2 points) ExWyP(x,y)

Q1) How many different 1-to-1 functions are there from a set with 6 elements to a...

Q1) How many different 1-to-1 functions are there from a set with 6 elements to a set with 6 elements ? Q2) Use Principle Mathematical Induction to prove that for all positive integers n. 7" + 4 +1 is divisible by 6
(6) Let A denote an m x n matrix. Prove that rank A < 1 if...

(6) Let A denote an m x n matrix. Prove that rank A < 1 if and only if A = BC. Where B is an m x 1 matrix and C is a 1 xn matrix. Solution (7) Do the following: (a) Use proof by induction to find a formula for for all positive integers n and for alld E R. Solution ... 2 for all positive (b) Find a closed formula for each entry of A" where A...
Let P be the power set of {a, b, c}. A function f: P , the...

Let P be the power set of {a, b, c}. A function f: P , the set of integers, follows: For A in P, f(A) = the number of elements in A. 1. Is f one-to-one? Explain. 2. Is f onto? Explain.

Part 15A and 15B (15) Let n E Z+,and let d be a positive divisor of...

Part 15A and 15B (15) Let n E Z+,and let d be a positive divisor of n. Theorem 23.7 tells us that Zn contains exactly one subgroup of order d, but not how many elements Z has of order d. We will determine that number in this exercise. (a) Determine the number of elements in Z12 of each order d. Fill in the table below to compare your answers to the number of integers between 1 and d that are...