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How To Use Truth Tables to Analyze Arguments

## To test the validity of an argument, we use the following three-step process

###
1. Symbolize each premise and the conclusion.

2. Make a truth table that has a column for each premise and a column for the conclusion.

3. If the truth table has a row where the conclusion column is FALSE while every premise column is TRUE, then the
argument is INVALID. Otherwise, the argument is VALID.

*This method is based upon the following:*

## Fundamental Principle of Argumentation

### An argument is INVALID if and only if it is logically possible for the conclusion to be false even though every premise is assumed to be true.

### Example 1

Use a truth table to test the validity of the following argument.

If you invest in the Gomermatic Corporation, then you get rich.

You didn't invest in the Gomermatic Corporation.

Therefore, you didn't get rich.

A. Valid

B. Invalid

see solution

### Example 2

Use a truth table to test the validity of the following argument.

If you are a hound dog, then you howl at the moon.

You don't howl at the moon.

Therefore, you aren't a hound dog.

A. Valid

B. Invalid

see solution

### Example 3

Use a truth table to test the validity of the following argument.

If I enter the poodle den, then I will carry my electric poodle prod or my can of mace.

I am carrying my electric poodle prod but not my can of mace.

Therefore, I will enter the poodle den.

A. Valid

B. Invalid

see solution

### Example 4

Test the validity of the following argument.

I will buy a new goat or a used Yugo.

If I buy both a new goat and a used Yugo, I will need a loan.

I bought a used Yugo and I don't need a loan.

Therefore, I didn't buy a new goat.

A. Valid

B. Invalid

see solution

### Example 5

Test the validity of the following argument.

Socrates has a new toga or he didn't waste 30 drachmas.

Plato has a pound of feta cheese or a quart of olive oil.

Socrates wasted 30 drachmas and Plato doesn't have a pound of feta cheese.

Therefore, Socrates has a new toga and Plato has a quart of olive oil.

A. Valid

B. Invalid

see solution

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