March 6, 2010

Here is the answer to the logic quiz I posted a week and one day ago.

The original statement took the form “If p, then q” where p: “the red car is broken” and q: “John drives the blue car.”

The only statement in a)-g) which is equivalent to that is statement c, which is the contrapositive of the original statement. The contrapositive takes the form “If not q, then not p.”

Reason: The original statement means exactly what it says: If the red car is broken, then John drives the blue car. Think if this as two circles, a smaller one inside a larger one. The larger outer circle is statement q: John drives the blue car. The smaller inner circle is p: the red car is broken. Whenever you are inside the circle p, then you are automatically inside circle q. There is no way out of this. You can, however, be inside circle q without being inside circle p. (Draw it out if you can’t visualize it.) What we can conclude from this is that if you are not inside circle q, then there is no way you can be inside circle p. Thus, if John is not driving the blue car, the red car is not broken.

There are other reasons why a, b, d, e, f, and g are false. If you can’t figure it out, post your question to the comments and I will be happy to answer it for you.

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