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: ...continues

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 tha ...continues

discrete structures

Let A = {1, 2, 3, 4, 5, 6, 12} and define the relation R on A by m R n iff m|n. Write the definitions of the properties, reflexive, antisymmetric and transitive and the use the definitions to determine whether each property holds for this relation. (a) Is this relation a partial ordering relation? Why? If so, draw its Hasse ...continues

transitive closures

I've attached the problem I'm having trouble with. I put the example I'm trying to work with in pink font. Please help! --- (See attached file for full problem description)

word problem - A person has 14 close friends.

A person has 14 close friends. (a) Suppose that two of her friends (of the 14 of either gender) do not like each other. If one of the two is invited, the other will not come to the party. How many ways are there to invite 8 people to the party. Explain. (b) Suppose that two of her friends are a couple. She cannot in ...continues

prove theta relation

Prove that theta is a reflexive, symmetric, and transitive relation; that is for all f, g, h: N to N, a. f belongs to theta f; b. f belongs to theta g then g belongs to theta f; c. f belongs to theta g and g belongs to theta h then f belongs to theta h;

logarithmic proof

From the definition of log, prove that: x to the log y power is equal to y to the log x power; ( x^log y = y ^ log x ) show all work!