Introduction to Logic
Given ¬(p ∨ q), use the Fitch system to prove (¬p ∧ ¬q).
Show Instructions
To apply a rule of inference, check the lines you wish to use as premises and click the button for the rule of inference. Reiteration allows you to repeat an earlier item. To delete one or more lines from a proof, check the desired lines and click Delete. When entering expressions, use Ascii characters only. Use ~ for ¬; use & for ∧; use  for ∨; use => for ⇒; use <=> for ⇔.
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~(p  q)
Premise
2
p
Assumption
3
p  q
Or Introduction
2
4
p => p  q
Implication Introduction
2
3
5
p
Assumption
6
~(p  q)
Reiteration
1
7
p => ~(p  q)
Implication Introduction
5
6
8
~p
Negation Introduction
4
7
9
q
Assumption
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p  q
Or Introduction
9
11
q => p  q
Implication Introduction
9
10
12
q
Assumption
13
~(p  q)
Reiteration
1
14
q => ~(p  q)
Implication Introduction
12
13
15
~q
Negation Introduction
11
14
16
~p & ~q
And Introduction
8
15
