each other, then the quadrilateral is not a parallelogram. If the diagonals of a quadrilateral bisect each other, then it is a parallelogram. . Validating Statements In this Section, we will discuss when a statement is true.
To answer this question, one must answer all the following questions. What does the statement mean? What would it mean to say that this statement is true and when this statement is not true? The answer to these questions depend upon which of the special words and phrases “and”, “or”, and which of the implications “if and only”, “if-then”, and which of the quantifiers “for every”, “there exists”, appear in the given statement.
Here, we shall discuss some techniques to find when a statement is valid. We shall list some general rules for checking whether a statement is true or not. Rule If p and q are mathematical statements, then in order to show that the statement “p and q” is true, the following steps are followed. Step- Show that the statement p is true.
Step- Show that the statement q is true. Rule Statements with “Or” If p and q are mathematical statements , then in order to show that the statement “ p or q ” is true, one must consider the following. Case By assuming that p is false, show that q must be true. Case By assuming that q is false, show that p must be true.
Rule Statements with “If-then” MATHEMATICS In order to prove the statement “if p then q ” we need to show that any one of the following case is true. Case By assuming that p is true, prove that q must be true.(Direct method) Case By assuming that q is false, prove that p must be false.(Contrapositive method) Rule Statements with “if and only if ” In order to prove the statement “ p if and only if q ”, we need to show. (i) If p is true, then q is true and (ii) If q is true, then p is true Now