Question

Prove or disprove the following statements. Remember to disprove a statement you have to show that the statement is false. Equivalently, you can prove that the negation of the statement is true. Clearly state it, if a statement is True or False. In your proof, you can use ”obvious facts” and simple theorems that we have proved previously in lecture.

(a) For all real numbers x and y, “if x and y are irrational, then x+y is irrational”.

(b) For all positive integers n, there is an even integer k such that 2n < k < 2n + 3

(c) Use proof by contraposition to show that, “for all real numbers a, if a^2 + 3 is irrational, then a is irrational”.

Answer 1