examples. Example Identify the type of “Or” used in the following statements and check whether the statements are true or false: is a rational number or an irrational number. To enter into a public library children need an identity card from the school or a letter from the school authorities. (iii) A rectangle is a quadrilateral or a -sided polygon.
Solution (i)The component statements are p : is a rational number. q : is an irrational number. Here, we know that the first statement is false and the second is true and “Or” is exclusive. Therefore, the compound statement is true.
The component statements are p: To get into a public library children need an identity card. q: To get into a public library children need a letter from the school authorities. Children can enter the library if they have either of the two, an identity card or the letter, as well as when they have both. Therefore, it is inclusive “Or” the compound statement is also true when children have both the card and the letter.
(iii) Here “Or” is exclusive. When we look at the component statements, we get that the statement is true. MATHEMATICS . .
Quantifiers Quantifiers are phrases like, “There exists” and “For all”. Another phrase which appears in mathematical statements is “there exists”. For example, consider the statement. p : There exists a rectangle whose all sides are equal.
This means that there is atleast one rectangle whose all sides are equal. A word closely connected with “there exists” is “for every” (or for all). Consider a statement. p: For every prime number p, p is an irrational number.
This means that if S denotes the set of all prime numbers, then for all the members p of the set S, p is an irrational number. In general, a mathematical statement that says “for every” can be interpreted as saying that all the members of the given set S where the property applies must satisfy that property. We should also observe that it is important to know precisely where in