Show:
\(P \rightarrow Q\)
4-Letter Words
Sequences and Sums
True or False
Counting
100
\(Q\rightarrow P\)
What is the converse?
100
The number of 4-letter words.
What is \(26^4\), or 456976?
100
1, 3, 6, 10, 15, 21, 28, ...
What are the Triangular numbers?
100
If a graph has chromatic number 5, then no matter how you draw it, there will be edges crossing.
What is True? This is the contrapositive of the 4-color theorem.
100

The numerical value of \({100 \choose 1}\)

What is 100?

200
\(\neg Q \rightarrow \neg P\)
What is the contrapositive?
200
The number of 4-letter words containing no repeated letters.
What is \(P(26,4)\), or 358800?
200
The recursive definition of the sequence \(2, 5, 7, 12, 19, 31,\ldots\)
What is \(a_n = a_{n-1} + a_{n-2}\); \(a_0 = 2\) and \(a_1 = 5\)?
200
\(\neg(P\rightarrow Q) \leftrightarrow (\neg P \rightarrow\neg Q)\)
What is False?
200

The number of subsets of \(\{0, 1, \ldots, 10\}\) of cardinality 3.

What is \( {11 \choose 3} \) (or \({11 \choose 8}\) or 165)?

300
\(P \wedge \neg Q\)
What is the negation?
300
The number of 4-letter words in which the letters are in alphabetical order.
What is \({29 \choose 4}\), or 23751?
300
A closed formula for \(1+3+5+7+\cdots + (2n+1)\)
What is \(n^2\)?
300
\((P \rightarrow Q) \vee P\)
What is True?
300

It's the chromatic number of `K_{2016, 2016}`.

What is `2`?

400
The negation of the converse of the contrapositive
What is \(\neg P \wedge Q\) or \(\neg (\neg P\rightarrow \neg Q)\)
400
The number of 4-letter words in which the letters are in alphabetical order with no repeats.
What is \({26 \choose 4}\), or 14950?
400
\[\sum_{k = 0}^{10} {10 \choose k}\]
What is \(2^{10}\)?
400
If \(|A \cup B| = 5\) then \(|A \cap B| \ne 5\) or \(|A| = 5\)
What is True?
400

The number of edges in a graph with 20 vertices all of degree 5.

What is 50? (\( \frac{20\cdot 5}{2} = 50 \))

500
An equivalent disjunction.
What is \(\neg P \vee Q\)
500
The number of 4-letter words which use all of the letters in "for'' (and no others).
What is \(36\), or \({4 \choose 2}\cdot 3!\)?
500

The closed formula of this sequence: 2, 3, 6, 11, 18, 27, ...

What is \( a_n = n^2 +2 \)?

500
If a graph contains exactly 3 vertices with odd degree, then the graph contains an Euler circuit.
What is True? (The hypothesis is false for all graphs.)
500

The number of ways to distribute 8 identical kegs of starfish ale to 4 local bars.

What is \( {11 \choose 3} \) (or \({11 \choose 8}\) or 165)?