Title Mathematical Reasoning - 4.pptx ✅

Mathematical Reasoning
MATHEMATICAL REASONING Implications Here we will discuss the implications of “if-then”, “only if” and “if and only if ”. For example, consider the statement. r: If you are born in some country, then you are a citizen of that country. When we look at this statement, we observe that it corresponds to two statements p and q given by p : you are born in some country. q : you are citizen of that country. Then the sentence “if p then q” says that in the event if p is true, then q must be true.
MATHEMATICAL REASONING One of the most important facts about the sentence “if p then q” is that it does not say any thing (or places no demand) on q when p is false. For example, if you are not born in the country, then you cannot say anything about q. To put it in other words” not happening of p has no effect on happening of q. Another point to be noted for the statement “if p then q” is that the statement does not imply that p happens.
MATHEMATICAL REASONING Let us consider another statement r: If a number is a multiple of 9, then it is a multiple of 3. Let p and q denote the statements p : a number is a multiple of 9. q: a number is a multiple of 3.