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)