Statement : Inverse :
If p à then q
If ~ p à then ~ q Is statement is TRUE , then Inverse if FALSE
Validating Statements (&)
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-1 Show that the statement p is true . Step-2 Show that the statement q is true .
Validating Statements ( 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 1 By assuming that p is false , show that q must be true . Case 2 By assuming that q is false , show that p must be true .
Validating Statements ( if -then )
In order to prove the statement “ if p then q ” we need to show that any one of the following case is true .
Case 1 By assuming that p is true , prove that q must be true .( Direct method )
Case 2 By assuming that q is false , prove that p must be false .( Contrapositive Method )