Give proof for the following statements. In writing your proofs, be sure to mimic the method shown in the lesson. Effort should be taken now to write mathematics that is acceptable to those reading...

Give proof for the following statements. In writing your proofs, be sure to mimic the method shown in the lesson. Effort should be taken now to write mathematics that is acceptable to those reading your work. 1) If x is an integer divisible by four, then x is the difference of two squares. 2) If two onto functions can be composed then their composition is onto. (Recall a function f: X?Y is onto if for every a in Y there is an element b in X for which f(b) = a.) 3) The square root of 2 is irrational. 4) There are an infinitely many primes. 5) The product ab of integers a and b is even if and only if at least one of the integers is even. 6) For all positive integers n, 1^2 + 2^2 + … + n^2 = (n)(n=1)(2n+1)/6.


Assignment: Proof Give proof for the following statements.   In writing your proofs, be sure to mimic the method shown in the lesson.   Effort should be taken now to write mathematics that is acceptable to those reading your work.   1) If x is an integer divisible by four, then x is the difference of two squares. 2) If two onto functions can be composed then their composition is onto. (Recall a function f: X(Y is onto if for every a in Y there is an element b in X for which f(b) = a.) 3) The square root of 2 is irrational. 4) There are an infinitely many primes. 5) The product ab of integers a and b is even if and only if at least one of the integers is even. 6) For all positive integers n, 1^2 + 2^2 + … + n^2 = (n)(n=1)(2n+1)/6.