# Conditional Statement: Truth Value

How to find the truth value of a conditional statement: its truth value, examples, and their solutions.

## Truth Value

True hypothesis (*p*) and false conclusion (*q*)

makes the conditional statement (*p* → *q*) false.

It's quite odd to think that

if *p* is false, then *p* → *q* is true.

But think of it this way:

If *p* is false,

then you can't be sure if *p* → *q* is false.

So just consider it to be true.

Conditional statement: hypothesis and conclusion

## Example 1

'*p*: 2 is a prime number' is true.

'*q*: 2 is a positive number' is true.

So '*p* → *q*' is true.

## Example 2

'*p*: 2 is a prime number' is true.

'*r*: 2 is an odd number' is false.

So '*p* → *r*' is false.

Remember:

true hypothesis and false conclusion

makes the conditional false.

## Example 3

'*r*: 2 is an odd number' is false.

So '*r* → *p*' is true.

You don't need to find the truth value of *p*,

(although you know that *p* is true)

because '*r* is true' is enough to make *r* → *p* true.