Formulae
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.
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.
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)
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