# Introduction of Validating Statements

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

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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.

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