Relations

Qu1) Is it true that ρ(A∪B)= ρ(A) ∪ ρ(B)? justify your answer. Qu2) Consider the function f:A→A defined by f(x)=x+1 and justify your answers. a) For A=Ν (integers) is f onto? b) For A=R(real number) is f injective? c) For A=Q (rationals) is f onto? d) For A=Z(all integers) is f a bije ...continues

Prove using induction

Prove using induction---Can someone show me how to do this? 1+α+α2+.......+αn-1=αn-1/a-1

Recurrence relation problem. Backwards substitution.

I need to know how to solve this problem: Solve the following recurrence relation: x(n) = 3x(n-1) for n > 1, x(1) = 4. It requires backwards substitution to solve.

How many one-to-one functions are there between A and B? If A has eight unique elements and B has ...

If A has eight unique elements and B has eight unique elements, how many one-to-one functions would there be? Also, I'd like to know how many there would be if A happened to have less elements than B or if B had less elements than A. Thank you for your time.

Binomial Theorem Identity Proof.

n + n + n + ..... = n + n + n + .... 0 2 4 1 3 5 (imagine the vertical sets of numbers are surrounded by a large parenthesis, as it is in a binomial expression) My problem: Prove the above expression for n = 2k. Thank you.

Set Operations: How many ways can a committee form from two groups of people.?

I have two committees A and B, with |A| = 3 = |B|, out of a group of 8 people such that at most one person can serve on both committees. How many ways we can form the committees A and B? Please show me how it's done.

How many possible onto functions are there between sets A and B? - I need to know how to get the number of possible onto functions (as opposed to the number of one-to-one functions) in between sets A and B: A: {1, 2, 3, 4, 5} B: {a, b, c}.

I need to know how to get the number of possible onto functions (as opposed to the number of one-to-one functions) in between sets A and B: A: {1, 2, 3, 4, 5} B: {a, b, c}. Please help if you can.

How do I solve these two summation problems?

I need to know how to get the results of: 1*3 + 2*4 + 3*5 + .... + n*(n+2) = ? and 1*3 + 3*5 + 5*7 + .... + (2n-1)*(2n+1) = ? Please help if you can. Thank you.

Linear Programming

A business dedicates to the import and sale of worn out coffee. The company concerns three types of coffee of select quality.: Colombian coffee, Honduran coffee and Dominican coffee. The company prepares three different mixtures in which it uses those three types of coffee. These mixtures are sold in bags of one pound. The three ...continues

Double Sum

Compute the double sum (see attached)