A = {1,2,3} and B = {a,b,c}, and let f: A B

A = {1,2,3} and B = {a,b,c}, and let f: A -> B (a) Give an example of a one to one function from A to B. Briefly explain why your example is a 1-1 function. (b) How many one to one functions from A to B are there? Explain. (c) Define a function f^-1, for some function f from A to B. (d) Is the function g: Z -> Z defined by g(n) = [n/2] a one to one function? Explain.

Solutions of the system of equations

Determine the solutions of the system of equations whose matrix is row equivalent to 1 0 −1 |1 0 1 3 |1 0 0 0 |0 Give three examples of the solutions. Verify that your solutions satisfy the original system of equations.

Relations on a set

Suppose that R and S are two relations on the set A = {a, b, c, d}, where R = {(a,b),(a,d),(b,c),(c,c),(d,a)}, and S = {(a,c),(b,d),(d,a)}. Find each of the following relations: a) R (+) S (Symmetric Difference) b) R^2 c) S^3 d) S o R (Composite)

word problem

Six friends discover the have a total of $21.61 with them. Show that one or more of them must have $3.61. (Hint, use the Pigeonhole Principle.)

word problem

I've attached the file. I need to know if I'm going in the right direction (in the red font), if not could you explain? (See attached file for full problem description) --- A person has 14 close friends. (a) How many ways can she invite 8 of her 14 close friends to a holiday get-together. Explain. (b) Suppose that out of her 14 friends 8 are women and 6 are men. (i) How many groups of 8 people can she invite that contain 5 women and 3 men? Explain. (ii) How many groups of 8 people can she invite that contain at least 1 man? Explain. (iii) How many groups of 8 people can be formed that contain at most 5 women? Explain. --- (See attached file for f... click for more