Advanced math a proof problem

Need help in the following proof problem. may need theorem and/ or definition. (See attached file for full problem description) --- Definition of Binomial Coefficient: Given a set X and a non-negative integer r, an r-subset of X is a subset A X of cardinality r. We denote the set of r-subsets of X by Pr(X), i.e. Pr(X) = {A X | |A| = r}. We define the binomial coefficient or binomial number ( n, r) (read 'n choose r') to be the cardinality of the set Pr(X) when |X| = n. The binomial Theorem: For all real numbers a and b and non-negative integers n, (a+b)n = n Sum (n, a(n-i) b(i) i=0 i) = an + …+ (n... click for more

Solve the system of equations

please solve this problem with detailed steps... --- Q5: Solve the system of equations 1 1 0 1 8 X1 2 -1 1 2 -1 0 X2 -1 -2 0 4 6 2 X3 2 0 -3 -1 1 4 0 X4 3 1 2 5-1 1 X5

Advanced math problem

(See attached file for full problem description) --- 1. Let p be a postive prime integer. Show that there is no rational number r such that p = r^2... ---

Advanced math exercise

(See attached file for full problem description) --- 2. Write the following as rational numbers: a) 0.731; (31 barred) b) 12.8697 (8697 barred) ---

Advanced math problem

Need help in determining the following proof exercise. (See attached file for full problem description) --- Corollary 14.2.4: If A is a denumerable set then so is A^n for every positive integer n. Proposition 14.2.3: If A and B are denumerable sets then so is their Cartesian product , AX B. ---