#### description

- Validating the Statements Involving the Connecting Words
- statement “p and q”, Statements with “Or”, Statements with “If-then”, Statements with “if and only if ”

#### notes

**Rule 1**- 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.

**Rule 2** - Statements with “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.

**Rule 3-** Statements with “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)

**Rule 4 -** Statements with “if and only if ”

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

Now we consider some examples.