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Logic Midterm
Dr. Lee Basham
In what follows we will discuss Validity, Soundness, Translation, basic Truth Tables, Logic gates, and basic rules of Natural deduction.
The hen finds wheat seeds and she collects them to grow wheat. The Hen asks the cat, the pig and the goose to help. The Hen plants the seeds. The Hen asks the cat, the pig and the goose to help. The seeds grow into wheat plants. The Hen harvests the Wheat. The Hen asks the cat, the pig and the goose to help. The Hen bakes delicious bread with delicious butter. The cat, the pig and the goose want to help eat the bread. The Red Hen says, if you did not help plant the seed, help harvest the wheat, help bake the bread, you get no bread.
Show q or t
Show r v q
Remember our rules of natural deduction (see your announcement notes, too): Remember, we can use these rules for different letters. s . t and so on…and remember, we use these rules to either eliminate or introduce connectives
p . q (or whatever letters)
p And elimination. .E
or if we like
q And (.) elimination .E
p v q
~p
q (Disjunctive Syllogism, DS)
or if you like,
p v q
~q
p DS
if p then q
p
q Modus ponens (MP) or if, then elimination
if p then q
~q
~p Modus Tollens (MT)
Here’s an introduction rule, where we introduce a connective,
p
p v q V introduction
Remember we can “or introduce” with any letter we want, and add any letter to it we want.
So let’s see what we can do with the above.
0 (F), 1 (T), output: 0 (F)
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