TOPICS

Formulae

Mathematical Reasoning

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

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