1) deductively valid (or just: valid) arguments;
2) inductively cogent arguments (or just: cogent).
Patterns of argument
Pattern 1 Pattern 2
1. AllAs are Bs. 1. Either P or Q.
2. x is anA. 2. ~Q (Q is false)
3. x is a B. 3. P.
In Example 3
1. Either Mike is in the cafeteria or Mike is in the library.
2. Mike isn’t in the cafeteria.
3. Mike is in the library
It is whole sentences that are repeated. The whole conclusion appears in the first
premise. So it is sentential logic.
Conjunction P and Q
Disjunction P or Q
Conditional If P then Q
Biconditional P if and only if Q
Note: the biconditional is the conjunction of ‘If P then Q’and ‘If Q then P’.
Argument By Elimination Conjunction
1. Either P or Q 1. P
2. ~P 2. Q
3. Q 3. P and Q
1. Either P or Q This shows that if two sentences are true,
2. ~Q then so is their conjunction.
Simplification Affirming theAntecedent (Modus
1. P and Q Ponens)
2. P 1. If P then Q
1. P and Q