\(P \rightarrow Q\)
4-Letter Words
Functions from \(A\) to \(Z\)
Sequences and Sums
True or False
100
\(Q\rightarrow P\)
What is the converse?
100
The number of 4-letter words.
What is \(26^4\), or 456976?
100
If every \(z\in Z\) has at most one \(a\in A\) with \(f(a)=z\) a function is said to be this.
What is injective (one-to-one)?
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.
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
If a function is a bijection, this relationship between \(|A|\) and \(|Z|\) must be true.
What is \(|A| = |Z|\)?
200
The sum of two consecutive triangular numbers.
What is a square number?
200
The negation of the contrapositive of a true implication.
What is False?
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
Let \(|A|=5\) and \(|Z|=6\). The number of surjective functions is this.
What is zero?
300
A closed formula for \(1+3+5+7+\cdots + (2n+1)\)
What is \(n^2\)?
300
\(\emptyset \subseteq \{2, 4, \{6, 8\}\}\)
What is True?
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
Let \(A=\{1,2,3,4\}\) and \(Z=\{a,b,c\}\). If \(f=\{(1,b),(2,a), (3,b), (4,c)\}\) \(f\) is this type of function.
What is surjective?
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?
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
I have 8 Apples to feed to my 3 Zebras, each zebra getting at most one apple. This must be the domain to interpret this as a function.
What are the 3 Zebras?
500
A binomial coefficient equal to the sum of the first 10 triangular numbers.
What is \({12 \choose 3}\)
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.)
M
e
n
u