Page 5 - LESSON NOTE

If N is divisible by 6, then N is divisible by 3

If N is divisible by 9, then N is divisible by 3

Inverse:

If N is not divisible by 6, then N is not divisible by 3

If N is not divisible by 9, then N is not divisible by 3

Statement: If p à then q

Inverse : If ~p à then ~q

Is statement is TRUE , then Inverse if FALSE

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.(Contra positive Method)

Validating Statements (if and only if)
In order to prove the statement “p if and only if q”, we need to show.

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