Discrete Mathematics Answers

Show that if a, b and c are real numbers and a=/= 0, then there is a unique solution of the equation ax+b=c.

Show that 5x+ 5y is an odd integer when x and y are integers of opposite parity.

14) Show that if the first 10 positive integers are placed around a circle, in any order, then there exist three integers in consecutive locations around the circle that have a sum of at least 17

3) Find a counterexample to the statement that every positive integer can be written as the sum of the squares of three integers.

Show that these statements about the real number x are equivalent:
(i)x is rational.
(ii)x/2 is rational.
(iii) 3x-1 is rational.

Show that these three statements are equivalent, where a and b are real numbers:
(i)a < b
(ii) The average of a and b is greater than a.
(iii) The average of a and b is less than b.

Prove that if n is a positive integer, then n is even if and only if 7n+ 4 is even.

(9) Show that at least three of any 25 days chosen must fall in the same month of the year

Prove that if n is an integer and 3n+ 2 is even, then n is even.

Prove that if x is rational and x=/= 0, then 1/x is rational.