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.

• If p is true, then q is true and
• If q is true, then p is true