Conditional Statements

What is a conditional statement?

Asserts a hypothetical relationship rather than a concrete fact

What conditions are involved in conditional statements?

Sufficient and Necessary

Which way do conditional statements go?

Sufficient - Necessary

What are the valid inferences?

1. Valid affirmation

2. Contrapositive

What is the contrapositive?

Flip & negate

What are the invalid inferences?

1. Fallacy of the converse

2. Fallacy of the inverse

What is the fallacy of the converse?

Try to switch both sides without negating

What is the fallacy of the inverse?

Try to negate both conditions without switching

What are sufficient condition keywords?

1. If

2. When

3. All

4. Any

5. Every

6. Each

7. The only

What are the necessary condition keywords?

1. Then

2. Only if

3. Only

4. Requires

What are the bi-conditional relationship keywords?

1. If and only if

2. If but only if

How are the bi-conditional relationship diagrammed

Double sided arrow

What conditional keywords demonstrate "If not"

1. Unless

2. Without

3. Until

4. Except

How do you deal with the word "no" in conditional statements?

No torpedo

What does the No Torpedo do?

Negates the concept at the end

Apply no torpedo to "No cats like being walked"

Cats do not like being walked

What is the Transitive Property?

If the necessary condition of one statement matches the sufficient condition of the other, then you can connect the statements

What is the Transitive Fallacy

An invalid conclusion where we don't have the necessary condition of one statement to match the sufficient condition of another

What does "and" turn into in the contrapositive?

"Or"