Conditional Statement: Truth Value

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 and false conclusion makes a conditional statement false. Otherwise, the conditional is true.

True hypothesis (p) and false conclusion (q)
makes the conditional statement (pq) false.

It's quite odd to think that
if p is false, then pq is true.

But think of it this way:
If p is false,
then you can't be sure if pq is false.

So just consider it to be true.

Conditional statement: hypothesis and conclusion

Example 1

The symbols represent statements: p: 2 is a prime number. q: 2 is a positive number. Find the truth value for p -> q.

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

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

So 'pq' is true.

Example 2

The symbols represent statements: p: 2 is a prime number. r: 2 is an odd number. Find the truth value for p -> r.

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

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

So 'pr' is false.

Remember:
true hypothesis and false conclusion
makes the conditional false.

Example 3

The symbols represent statements: p: 2 is a prime number. r: 2 is an odd number. Find the truth value for r -> p.

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

So 'rp' 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 rp true.