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 : Symmetric Difference and Composite

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 proof

Six friends discover they 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

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 diagram. (b)Write the (Boolean, that is, the yes/no) matrix of this relation.