A mathematical statement is a meaningful sentence that has a definite state of being true or false. If > 0, then 2 > 0. * an open sentence is a sentence which can be a statement if its variables are defined with appropriate values. A proof establishes the truth of a given statement beyond doubt. Statement: for every real number , 2 + 1 2 . Thus, ( 1) is also a real number. So, 2 + 1 2 as required. Implications have the form if a, then b where a and b are themselves statements and are written as a => b . A is called the hypothesis and b is called the conclusion. When proving an implication, statement a is be assumed to be true and is used to prove that statement b is true. Ad + cd < bc + cd. D(a + c) < c(b + d) a+c b+d.
