State whether the “Or” used in the following statements is “exclusive “or” inclusive. Give reasons for your answer. Sun rises or Moon sets. To apply for a driving licence, you should have a ration card or a passport.
(iii) All integers are positive or negative. . Implications In this Section, we shall discuss the implications of “if-then”, “only if” and “if and only if ”. The statements with “if-then” are very common in mathematics.
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. 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. There are several ways of understanding “if p then q” statements. We shall illustrate these ways in the context of the following statement. r: If a number is a multiple of , then it is a multiple of .
Let p and q denote the statements p : a number is a multiple of . q: a number is a multiple of . MATHEMATICS Then, if p then q is the same as the following: . p implies q is denoted by p ⇒ q .
The symbol ⇒ stands for implies. This says that a number is a multiple of