|Class 11 Maths Mathematical Reasoning||Validating Statements|
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)
Validating Statements (if and only if)
In order to prove the statement “p if and only if q”, we need to show.
Validate by contradiction
We assume that p is not true i.e. ∼p is true. Then, we arrive at some result which contradicts our assumption. Therefore, we conclude that p is true.