Chapter Two, Tutorial 4
Deductive Concepts

 

Remember how we defined valid? Think about it for a moment: an argument is valid if and only if what? (Pick one.)

 

Right.

An argument is valid just in case it is not possible that its conclusion be false while its premises are all true.

And our first example about Chris (remember: he'll get an 'A' or a 'B', but not an 'A' it turns out) is pretty clear in this:

AvB
~A 
  B   

If you think about it a minute, you'll see that given how we've defined the possibilities for our connectives to be true, there is no way for B to be false (given the premises); it is inescapable.

 

 

 

 

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Remember that we defined logical equivalence or sameness of meaning in terms of impossibility. Two sentences are logically equivalent iff what?

  1. it is impossible for each sentence to be false.
  2. it is impossible for one sentence to be true while the other is false.
  3. it is impossible for one sentence of the pair to be false.

Hint: We've defined this one