Philosophy question about logic- methods of deduction?

Question

This problem needs to be expanded using elementary valid argument forms. 

1. If not Z then R
2. If (not Z and R) then T
Therefor if not Z then T

Can anyone help? I'm studying for a quiz and can't quite figure this out. I need the name of each rule of inference used. Thanks in advance guys.

Ex Falso Quodlibet · Accepted Answer

Hi

Here are a couple of deductions:

1. ~Z > R  Premise
2. (~Z & R) > T  Premise
3. ~Z > (~Z & R)  1 Absorption
4. ~Z > T  3,2 Hypothetical Syllogism

Using a different system:

(1) 1. ~Z > R  Premise
(2) 2. (~Z & R) > T  Premise
(3) 3. ~Z  Assumption
(1,3) 4. R  1,3 MP
(1,3) 5. ~Z & R  3,4 &I
(1,2,3) 6. T  2,5 MP
(1,2) 7. ~Z > T  3,6 CP

? · Answer

if not yes then no 
if (not yes and no) then maby
therefor if not yes then maby

the flaw is here that it could also be no instead of maby

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Philosophy question about logic- methods of deduction?

2 Answers