Prove the statements that are true and give counterexample to disprove those that are false

Prove the statements that are true and give counterexample to disprove those that are false. For all integers n, if n is prime then (-1)^n=-1 (READ:...then (-1) to the n power equal -1)

Using Permutations and Combinations

How many distinct nonnegative integer solutions are there to the equation x1 + x2 + x3 =7 in which x1 is greater than or equal to 3.

Using Permutations and Combinations

Can you check my answers and help me with B? Preparing a plate of cookies for 8 children, 3 types cookies {chocolate chip, peanut butter, oatmeal}, unlimited amount of cookies in supply but only cookie per child. One cookie per plate, one plate per child. A) How many different plates can be prepared? C(8,3) = 56 B) ...continues

Principle Of Inclusion and Exclusion

let IU - intersection U - union Write an expression for the number of terms in the expansion of |A1 U ... U An| given in equ Sum 1<=i

Cannot Work this one

In the questions below suppose the variable x represents students and the variable y represents courses, and A(y): y is an advanced course S(x): x is a sophomore F(x): x is a freshman T(x,y): x is taking y. Write the statement using these predicates and any needed quantifiers. a. There is a course that every freshman is ...continues

I am stumped

This question has three parts: So I am making it 5 credits for that reason. a. Show that the hypotheses "I left my notes in the library or I finished the rough draft of the paper" and "I did not leave my notes in the library or I revised the bibliography" imply that "I finished the rough draft of the paper or I revised the bi ...continues

Relations

S = {0, 1, 2, 4, 6} Test the binary relations on S for reflexivity, symmetry ,antisymmetry, and transitivity. Also find the reflexive, symmetric and transitive closure of each relations. A) P = {(0,0), (1,1), (2,2), (4,4), (6,6), (0,1), (1,2), (2,4), (4,6) } B) P {(0,1), (1,0), (2,4), (4,2), (4,6), (6,4)} C) P ((0 ...continues

Relations

Test the binary relations on S for reflexivity, symmetry ,antisymmetry, and transitivity A) S = Q X p Y <-> ABS(X) <= ABS(Y) B) S = Z X p Y <-> x -y is an integral multiple of 3 C) S = N X P Y <-> X is odd D) S = Set of all squares in the place S1 p S2 <-> length of side of S1 = length of side S2 E) ...continues

Relations

For each case, think of a set S and a binary relation p on S for - A. p is reflexive and symmetric but not transitive b. p is reflexive and transitive but not symmetric c. p is reflexive but neither symmetric nor transitive

Functions

Let P be the power set of {A, B} and let S be the set of all binary strings of length 2. A function f: P -> S is defined as follows: For A in P, f(A) has a 1 in the high-order bit position (left end of string) if and only if a is in A. f(A) has a 1 in the low-order bit position (right end of string) if and only if b is in A. Is ...continues