Disjunctive syllogism is the rule that we use when we have a disjunction in a logical argument. If we want to write out a sentence and use disjunctive syllogism, it’ll look like this: “This is either chocolate cake or vanilla cake. This is not vanilla cake.”
Now, if you remember, or means that you’ll either have this, but if you can’t have this, you’ll have that. So in this case, the logical conclusion would be that “This is chocolate cake”, since it’s not vanilla cake.
If we were to symbolize it, the sentence would look like this:
- C v V
- ~V
- .*. C
So as you can see, disjunctive syllogism is pretty easy. This is literally all there is to it.
Another two things I want to mention is the simplification rule and adjunction rule. The adjunction rule says that if you have something like this:
P
Q
Then the following conclusion will look like this:
.*. P^Q
Simplification is just the opposite of adjunction, and what you do is just break up the conjunction into its parts.
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