Use Principle of Inclusion and Exclusion to determine: a) # of all possible bit-strings of length 8 either starting with 1 or end with 00 b) # of all positive integers less than 1000 that are divisible by 7 but not by 11 Show that the square of an even number is an even number, using the direct proof. Show that, if n is an integer and n^3 + 5 is odd, then n is even, using: a) Contraposition b) Contradiction Find a counter example to the statement that every positive integer can be written as the sum of the squares of three integers. Prove that 2^n > n^2 for n greaterthanorequalto 5 elementof N What is wrong with the following "proof? Show that "all horses are the same color