This is the archive for Math.
- Answer to Logic Quiz
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.
- Logic Quiz
Here is a little logic quiz for you:
Given this statement, which of the following is correct?
List your answer in the comments. (The answer can be any combination of the statements.)
Statement: If the red car is broken, then John drives the blue car.
a) John drives the blue car only if the red car is broken.
b) If the red car is not broken, then John does not drive the blue car.
c) If John does not drive the blue car, then the red car is not broken.
d) If John drives the blue car, then the red car must be broken.
e) The red car is broken only if John drives the blue car.
f) John drives the blue car if and only if the red car is broken.
g) If John drives the red car, the blue car is broken.
- Palindrome Dates
I didn’t have time to post about it yesterday, but yesterday’s date was a palindrome! (For those of you who don’t know, a palindrome is something that reads the same backward as it does forward- Yesterday’s date was 01022010.) It was only the second palindrome date of the 21st century. The first was 10022001 (October 2, 2001), and before that the last palindrome date was August 31, 1380! (Note: I am talking about palindromes of the form MMDDYYYY or YYYYMMDD. Both of these forms, when reversed on the dates listed below, read the same.)
Though palindrome dates are pretty rare, there will be 12 in the 21st century. When there is a new millennia, it turns out there are usually 12 palindrome dates each century–one for each month–for the first two centuries. The exception to this was in the 1300s, which only had 7 and was the third century of that millennium.
Anyway, while I was waiting for my food at a restaurant last night, I took a moment and figured out the 12 palindrome dates of this century. Two have already passed, so 10 remain.
Here are the ones for the 21st century: