Question 1

ﬁnd a formula that generates the following sequence a1, a2, a3 . . . .
-2, 0, 2, 0, 2, 0, 2, . . .

Accepted Answer

The answer of ﬁnd a formula that generates the following...

Question 2

Consider these functions from the set of licensed drivers in the state of New York. Is a function one-to-one if it assigns to a licensed driver his or her (a) birthdate (b) mother's ﬁrst name (c) drivers license number?

Accepted Answer

(a) No (b)

Question 3

ﬁnd a formula that generates the following sequence a1, a2, a3 . . . .
-0, 2, 0, 2, 0, 2, 0, . . .

Accepted Answer

The answer of ﬁnd a formula that generates the following...

Question 4

suppose A = {a, b, c} and B = {b, {c}}. Mark the statement TRUE or FALSE.
-$$\{ b , c \} \in \mathcal { P } ( A )$$

Accepted Answer

A) True 
 B)False

Question 5

Suppose $f : \mathbf { N } \rightarrow \mathbf { N }$ has the rule $f ( n ) = 4 n ^ { 2 } + 1$ . Determine whether $f$ is onto $\mathbf { N }$

Accepted Answer

The answer of Suppose \(f : \mathbf { N }...

Question 6

suppose A = {1, 2, 3, 4, 5}. Mark the statement TRUE or FALSE.
-$$( 1,1 ) \in A \times A$$

Accepted Answer

A) True 
 B)False

Question 7

Let $\mathbf { A } = \left( \begin{array} { c c } 
1 & m \
0 & 1
\end{array} \right)$ . Find $\mathbf { A } ^ { n }$ where n is a positive integer.

Accepted Answer

\[\mathbf { A } ^ {

Question 8

mark each statement TRUE or FALSE. Assume that the statement applies to all sets.
-$$\text { If } A \cap B = A \cup B \text {, then } A = B$$

Accepted Answer

A) True 
 B)False

Question 9

Find the sum 112 + 113 + 114 + · · · + 673.

Accepted Answer

The answer of Find the sum 112 + 113 +...

Question 10

Suppose $f : \mathbf { N } \rightarrow \mathbf { N }$ has the rule $f ( n ) = 3 n ^ { 2 } - 1$ . Determine whether $f$ is 1-1 .

Accepted Answer

The answer of Suppose \(f : \mathbf { N }...

ﬁnd a formula that generates the following sequence a1, a2, a3 . . . . -2, 0, 2, 0, 2, 0, 2, . . .

Consider these functions from the set of licensed drivers in the state of New York. Is a function one-to-one if it assigns to a licensed driver his or her (a) birthdate (b) mother's ﬁrst name (c) drivers license number?

ﬁnd a formula that generates the following sequence a1, a2, a3 . . . . -0, 2, 0, 2, 0, 2, 0, . . .

suppose A = {a, b, c} and B = {b, {c}}. Mark the statement TRUE or FALSE. - $\{ b , c \} \in \mathcal { P } ( A )$

Suppose $f : \mathbf { N } \rightarrow \mathbf { N }$ has the rule $f ( n ) = 4 n ^ { 2 } + 1$ . Determine whether $f$ is onto $\mathbf { N }$

suppose A = {1, 2, 3, 4, 5}. Mark the statement TRUE or FALSE. - $( 1,1 ) \in A \times A$

Let $\mathbf { A } = \left( \begin{array} { c c } 1 & m \\0 & 1\end{array} \right)$ . Find $\mathbf { A } ^ { n }$ where n is a positive integer.

mark each statement TRUE or FALSE. Assume that the statement applies to all sets. - $\text { If } A \cap B = A \cup B \text {, then } A = B$

Find the sum 112 + 113 + 114 + · · · + 673.

Suppose $f : \mathbf { N } \rightarrow \mathbf { N }$ has the rule $f ( n ) = 3 n ^ { 2 } - 1$ . Determine whether $f$ is 1-1 .

The Foundations: Logic and Proofs

A: the Foundations: Logic and Proofs

Basic Structures: Sets, Functions, Sequences, Sums, Matrices

Algorithms

A: Algorithms

Number Theory and Cryptography

A: Number Theory and Cryptography

Induction and Recursion

A: Induction and Recursion

Counting

A: Counting

Discrete Probability

A: Discrete Probability

Advanced Counting Techniques

A: Advanced Counting Techniques

Relations

A: Relations

Graphs

A: Graphs

Trees

A: Trees

Boolean Algebra

A: Boolean Algebra

Modeling Computation

A: Modeling Computation

Mathematics Problem Set: Set Theory, Number Theory, Combinatorics, and Boolean Algebra

Filters

Exam 2: A: Basic Structures: Sets, Functions, Sequences, Sums, Matrices

ﬁnd a formula that generates the following sequence a1, a2, a3 . . . . -2, 0, 2, 0, 2, 0, 2, . . .

Consider these functions from the set of licensed drivers in the state of New York. Is a function one-to-one if it assigns to a licensed driver his or her (a) birthdate (b) mother's ﬁrst name (c) drivers license number?

ﬁnd a formula that generates the following sequence a1, a2, a3 . . . . -0, 2, 0, 2, 0, 2, 0, . . .

suppose A = {a, b, c} and B = {b, {c}}. Mark the statement TRUE or FALSE. - {b,c}∈P(A)\{ b , c \} \in \mathcal { P } ( A ){b,c}∈P(A)

Suppose f:N→Nf : \mathbf { N } \rightarrow \mathbf { N }f:N→N has the rule f(n)=4n2+1f ( n ) = 4 n ^ { 2 } + 1f(n)=4n2+1 . Determine whether fff is onto N\mathbf { N }N

suppose A = {1, 2, 3, 4, 5}. Mark the statement TRUE or FALSE. - (1,1)∈A×A( 1,1 ) \in A \times A(1,1)∈A×A

Let A=(1m01)\mathbf { A } = \left( \begin{array} { c c } 1 & m \\0 & 1\end{array} \right)A=(10​m1​) . Find An\mathbf { A } ^ { n }An where n is a positive integer.

mark each statement TRUE or FALSE. Assume that the statement applies to all sets. - If A∩B=A∪B, then A=B\text { If } A \cap B = A \cup B \text {, then } A = B If A∩B=A∪B, then A=B

Find the sum 112 + 113 + 114 + · · · + 673.

Suppose f:N→Nf : \mathbf { N } \rightarrow \mathbf { N }f:N→N has the rule f(n)=3n2−1f ( n ) = 3 n ^ { 2 } - 1f(n)=3n2−1 . Determine whether fff is 1-1 .

The Foundations: Logic and Proofs

A: the Foundations: Logic and Proofs

Basic Structures: Sets, Functions, Sequences, Sums, Matrices

Algorithms

A: Algorithms

Number Theory and Cryptography

A: Number Theory and Cryptography

Induction and Recursion

A: Induction and Recursion

Counting

A: Counting

Discrete Probability

A: Discrete Probability

Advanced Counting Techniques

A: Advanced Counting Techniques

Relations

A: Relations

Graphs

A: Graphs

Trees

A: Trees

Boolean Algebra

A: Boolean Algebra

Modeling Computation

A: Modeling Computation

Mathematics Problem Set: Set Theory, Number Theory, Combinatorics, and Boolean Algebra

Filters

suppose A = {a, b, c} and B = {b, {c}}. Mark the statement TRUE or FALSE. - $\{ b , c \} \in \mathcal { P } ( A )$

Suppose $f : \mathbf { N } \rightarrow \mathbf { N }$ has the rule $f ( n ) = 4 n ^ { 2 } + 1$ . Determine whether $f$ is onto $\mathbf { N }$

suppose A = {1, 2, 3, 4, 5}. Mark the statement TRUE or FALSE. - $( 1,1 ) \in A \times A$

Let $\mathbf { A } = \left( \begin{array} { c c } 1 & m \\0 & 1\end{array} \right)$ . Find $\mathbf { A } ^ { n }$ where n is a positive integer.

mark each statement TRUE or FALSE. Assume that the statement applies to all sets. - $\text { If } A \cap B = A \cup B \text {, then } A = B$

Suppose $f : \mathbf { N } \rightarrow \mathbf { N }$ has the rule $f ( n ) = 3 n ^ { 2 } - 1$ . Determine whether $f$ is 1-1 .