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) How many different plates can be prepared if at least one of each kind of cookie is given out ? C) How many different plates can be prepared if no one likes oatmeal? C(8,2) = 28 D) How many different plates can be prepared if two children need to get peanut butter? C(6,3) = + C(2,1) = 22 E) How many different plates can be prepared if the dog got into the kitche... click for more

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 taking. b. Some freshman is taking an advanced course.