Lesson LOGIC PROBLEM INVOLVING IF I AM HUNGRY THEN I WILL EAT WITH SOLUTION AND EXPLANATION

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PROBLEM

Determine if the argument is valid or invalid. give a reason to justify your answer.

If I am  hungry, then I will eat.
I am not hungry.
Therefore, I will not eat.

SOLUTION

This involves the use of the implies statement.

There are three additional statements that pertain to the implied statement.

They are:

The inverse to the implied statement.
The converse to the implied statement.
The contra-positive to the implied statement.

Only the contra-positive to the implied statement is equivalent to the implied statement.

You cannot assume that the inverse to the implied statement is equivalent to the implied statement.  If you do so, then you are committing the fallacy of the inverse.

You cannot assume that the converse to the implied statement is equivalent to the implied statement.  If you do so, then you are committing the fallacy of the converse.

Your problem statement is:

If I am  hungry, then I will eat.
I am not hungry.
Therefore, I will not eat.

This involves the use of the statement called the inverse of the implied statement.

The implied statement is:
If I am hungry, then I will eat.

The inverse of the implied statement is:
If I will not eat, then I am not hungry.

The statements are not equivalent.
If you assume they are equivalent, then you are committing the fallacy of the inverse.

This can be proven through the use of truth tables.

The proof can be found here:

<a href = "http://www.algebra.com/algebra/homework/Conjunction/THEO-2011-08-22-02.lesson" target = "_blank">PROOF OF THE FALLACY OF THE INVERSE</a>

Some additional information regarding laws and statements can be found here:

<a href = "http://www.algebra.com/algebra/homework/Conjunction/THEO-061210.lesson" target = "_blank">STATEMENT LAWS AND FALLACIES</a>

In other words, the argument is invalid by reason of the fallacy of the inverse.