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

**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.

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