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Chapter 4

Chapter 4 Necessary and Sufficient Conditions

Conditional Statements

4.1 Sufficient condition

- A is sufficient for B if A is true, then B is true.

4.2 Necessary condition

- X is necessary condition for Y: if X is not true, Y is not true.

4.3 Relationship between Necessary and sufficient conditions.

- A is sufficient for B = B is necessary for A.

4.4 All and only

- All A’s are B’s

= A is sufficient for B

= B is necessary for A

- Only X’s are Y’s

= X is necessary for Y

= Y is sufficient for X

4.5 If and only if

- Antecedent comes immediately after the, if.

- Consequent is the necessary condition.

- ALL OF THE FOLLOWING MEAN THE SAME THING:

If S, then N

N, if S

S only if N

Only S if N

- If you are a student, then you’re a human.

- You’re human if you’re a student.

- You’re a student only if you’re a human.

- Being a student is sufficient for being human.

- Being human is necessary for being a student.

4.6 Unless

- Not A unless B =B is necessary for A.

- A unless B = B is necessary for not A.

4.7 Good conditional arguments

- Affirm the sufficient condition (Modus ponens)

- Deny the necessary condition (Modus tollens)

- “Affirm” means “say the same thing”

- “Deny” means “say the opposite”

4.8 Bad Conditional arguments

- Deny the sufficient condition.

- Affirm the necessary condition.

4.9 Conditional indicator words.

- If… then, if, only if, all, only, unless.

4.10 Valid arguments.

- In valid argument, if the premises are true, the conclusion must be true. However, these arguments can

still be unacceptable, because of the false of irrelevant premises. Validity is necessary but not sufficient,

for acceptation a deductive argument.

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