# Logical Argument

Is the conclusion true here?

Either Peter did not know it or Sarah did know it. But Peter did know it. Therefore, Sarah did know it.

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This won't get you anywhere. Language is not logic. Unlike symbols in formal logic that are, by design, unambiguous, words in natural languages are, by design, ambiguous. In fact a word can, and often does, mean the exact opposite of itself. That includes "either... or". If you ask me, your conclusion is neither correct nor incorrect — it is not a conclusion in the first place, it's a non sequitur. – RegDwigнt Jun 26 '13 at 9:07

## 1 Answer

There are four cases:

Case 1: Sarah and Peter both know it.
Case 2: Sarah and Peter both do not know it.
Case 3: Sarah knows it but Peter does not.
Case 4: Peter knows it but Sarah does not.

We are given "Either Peter did not know it or Sarah did know it". This rules out case 4.

We are now told "But Peter did know it". This rules out cases 2 and 3.

Since 2, 3, and 4 are ruled out, case 1 must be correct. So the conclusion is correct, Sarah and Peter must both know it, hence Sarah must know it.

(The above assumes the "or" is intended to be inclusive. The final result is the same if you understand it to be exclusive, though the reasoning is slightly different -- case 3 is ruled out earlier.)

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Thanks. That was very useful – user40011 Jun 26 '13 at 9:04