Question 1

Use De Morgan's laws to write the negation of the statement. The towel is wet or it isn't striped.

Accepted Answer

A)  The towel is not wet and it is striped. 
B)  The towel is not wet or it is striped. 
C)  The towel is not wet or it isn't striped. 
D)  The towel is not wet and it isn't striped. 
A)  The towel is not wet and it is striped. 
B)  The towel is not wet or it is striped. 
C)  The towel is not wet or it isn't striped. 
D)  The towel is not wet and it isn't striped. A

Question 2

Draw an Euler circle diagram for the statement.
All kittens are cats.
A)

B)

C)

D)

Accepted Answer

C

Question 3

Determine if the two statements are logically equivalent, negations, or neither.
$$p \rightarrow \sim q ; q \rightarrow \sim p$$

Accepted Answer

A)  Negations 
B)  Neither 
C)  Logically equivalent 
A)  Negations 
B)  Neither 
C)  Logically equivalent C

Question 4

A new weight loss supplement claims that if you take this product daily and you cut your calorie intake by 10%, you will lose at least 10 pounds in the next 4 months. If you use the product daily and you don't cut your calorie intake by 10%, and then don't lose 10 pounds, is the claim made by the advertiser true or false?

Accepted Answer

A) True 
 B)False

Question 5

Let p = "Paolo bicycles to school." Let q = "Roberto drives to school." Write the following statement in symbols. Paolo does not bicycle to school, or Roberto drives to school.

Accepted Answer

The answer of Let p = "Paolo bicycles to school."...

Question 6

Let p = "Sally is three years old." Let q = "Sally's mom is thirty." Write the following statement in words. $$\sim q \rightarrow p$$

Accepted Answer

If Sally's mom is no

Question 7

Find the contrapositive of the statement.
$$p \rightarrow \sim q$$
A) $\sim p \rightarrow \sim q$
B) $\sim q \rightarrow p$
C) $q \rightarrow \sim p$
D) $\sim p \rightarrow q$

Accepted Answer

The answer of Find the contrapositive of the statement.
\[p \rightarrow...

Question 8

State whether the sentence is a statement or not. Close the door.

Accepted Answer

The answer of State whether the sentence is a statement...

Question 9

Write the converse of the conditional statement. I will buy a new computer if my laptop breaks.

Accepted Answer

A)  If my laptop doesn't break, then I won't buy a new computer. 
B)  If I don't buy a new computer, then my laptop will break. 
C)  If I buy a new computer then my laptop will break 
D)  If I don't buy a new computer, then my laptop won't break. 
A)  If my laptop doesn't break, then I won't buy a new computer. 
B)  If I don't buy a new computer, then my laptop will break. 
C)  If I buy a new computer then my laptop will break 
D)  If I don't buy a new computer, then my laptop won't break.

Question 10

$$\begin{array}{l}
\text { Complete the following truth table. }\
\begin{array} { c | c | c | c | c } 
p & q & r & ( q \wedge \sim r ) & ( q \wedge \sim r ) \leftrightarrow p \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } & & \
\mathrm { T } & \mathrm { T } & \mathrm { F } & & \
\mathrm { T } & \mathrm { F } & \mathrm { T } & & \
\mathrm { T } & \mathrm { F } & \mathrm { F } & & \
\mathrm { F } & \mathrm { T } & \mathrm { T } & & \
\mathrm { F } & \mathrm { T } & \mathrm { F } & & \
\mathrm { F } & \mathrm { F } & \mathrm { T } & & \
\mathrm { F } & \mathrm { F } & \mathrm { F } & &
\end{array}
\end{array}$$

Accepted Answer

The answer of \[\begin{array}{l}
\text { Complete the following truth table....

Question 11

Determine if the two statements are logically equivalent, negations, or neither.
$$\sim p \rightarrow q ; \sim p \vee q$$

Accepted Answer

A)  Negations 
B)  Logically equivalent 
C)  Neither 
A)  Negations 
B)  Logically equivalent 
C)  Neither

Question 12

Determine whether the following argument is valid, using the given forms of valid arguments and fallacies.
$\begin{array} { l } 
\sim p \vee q \
\sim q \
\hline \therefore \sim p
\end{array}$

Accepted Answer

A)  Valid 
B)  Invalid 
A)  Valid 
B)  Invalid

Question 13

Determine the validity of the following argument.
$\begin{array} { l } 
q \rightarrow \sim p \
\frac { q } { \therefore \sim p }
\end{array}$

Accepted Answer

A)  Valid 
B)  Invalid 
A)  Valid 
B)  Invalid

Question 14

Write the contrapositive of the conditional statement. If I get a speeding ticket, my parents do not pay for my insurance.

Accepted Answer

A)  If my parents do not pay for my insurance, I get a speeding ticket. 
B)  If I get a speeding ticket, my parents pay for my insurance. 
C)  If I do not get a speeding ticket, my parents pay for my insurance. 
D)  If my parents pay for my insurance, I do not get a speeding ticket. 
A)  If my parents do not pay for my insurance, I get a speeding ticket. 
B)  If I get a speeding ticket, my parents pay for my insurance. 
C)  If I do not get a speeding ticket, my parents pay for my insurance. 
D)  If my parents pay for my insurance, I do not get a speeding ticket.

Question 15

Identify the statement as a conjunction, disjunction, conditional, or biconditional. We will build a pool if and only if we win the lottery.

Accepted Answer

A)  Conditional 
B)  Conjunction 
C)  Biconditional 
D)  Disjunction 
A)  Conditional 
B)  Conjunction 
C)  Biconditional 
D)  Disjunction

Question 16

Decide whether each statement is simple or compound. i. If you win the next round, you will be a finalist.
ii. She is not feeling well.
iii. $7 + 2 = 14$
iv. He is taking history and economics.

Accepted Answer

Compound,

Question 17

Use a truth table to determine whether the argument is valid.
$$\begin{array} { l } 
p \wedge q \
\sim p \vee \sim q \
\hline \therefore \sim p
\end{array}$$

Accepted Answer

The answer of Use a truth table to determine whether...

Question 18

Determine if the two statements are logically equivalent, negations, or neither.
$$( p \vee q ) \wedge \sim r ; \sim ( p \wedge q ) \vee r$$

Accepted Answer

A)  Neither 
B)  Logically equivalent 
C)  Negations 
A)  Neither 
B)  Logically equivalent 
C)  Negations

Question 19

Is the following sentence a statement? Neither Ben nor Alonzo is going camping.

Accepted Answer

The answer of Is the following sentence a statement? Neither...

Question 20

Use a truth table to determine whether the argument is valid.
$\begin{array}{l}
\sim p \wedge q \
\frac{r \rightarrow \sim q}{\therefore r}
\end{array}$

Accepted Answer

The answer of Use a truth table to determine whether...

Use De Morgan's laws to write the negation of the statement. The towel is wet or it isn't striped.

Draw an Euler circle diagram for the statement. All kittens are cats. A) B) C) D)

Determine if the two statements are logically equivalent, negations, or neither. $p \rightarrow \sim q ; q \rightarrow \sim p$

Let p = "Paolo bicycles to school." Let q = "Roberto drives to school." Write the following statement in symbols. Paolo does not bicycle to school, or Roberto drives to school.

Let p = "Sally is three years old." Let q = "Sally's mom is thirty." Write the following statement in words. $\sim q \rightarrow p$

Find the contrapositive of the statement. $p \rightarrow \sim q$ A) $\sim p \rightarrow \sim q$ B) $\sim q \rightarrow p$ C) $q \rightarrow \sim p$ D) $\sim p \rightarrow q$

State whether the sentence is a statement or not. Close the door.

Write the converse of the conditional statement. I will buy a new computer if my laptop breaks.

Complete the following truth table. p q r (q\wedge\simr) (q\wedge\simr)\leftrightarrowp

Determine if the two statements are logically equivalent, negations, or neither. $\sim p \rightarrow q ; \sim p \vee q$

Determine whether the following argument is valid, using the given forms of valid arguments and fallacies. \simp\veeq \simq \therefore\simp

Determine the validity of the following argument. q\rightarrow\simp

Write the contrapositive of the conditional statement. If I get a speeding ticket, my parents do not pay for my insurance.

Identify the statement as a conjunction, disjunction, conditional, or biconditional. We will build a pool if and only if we win the lottery.

Decide whether each statement is simple or compound. i. If you win the next round, you will be a finalist. ii. She is not feeling well. iii. $7 + 2 = 14$ iv. He is taking history and economics.

Use a truth table to determine whether the argument is valid. p\wedgeq \simp\vee\simq \therefore\simp

Determine if the two statements are logically equivalent, negations, or neither. $( p \vee q ) \wedge \sim r ; \sim ( p \wedge q ) \vee r$

Is the following sentence a statement? Neither Ben nor Alonzo is going camping.

Use a truth table to determine whether the argument is valid. \simp\wedgeq

Problem Solving

Set

Numeration Systems

The Real Number System

Topics in Algebra

Consumer Mathematics

Measurement

Geometry

Probability and Counting Techniques

Statistics

Voting Methods

Graph Theory

Available Online: Other Mathematical Systems

Summary

Filters

Exam 3: Logic

Use De Morgan's laws to write the negation of the statement. The towel is wet or it isn't striped.

Draw an Euler circle diagram for the statement. All kittens are cats. A) B) C) D)

Determine if the two statements are logically equivalent, negations, or neither. p→∼q;q→∼pp \rightarrow \sim q ; q \rightarrow \sim pp→∼q;q→∼p

Let p = "Paolo bicycles to school." Let q = "Roberto drives to school." Write the following statement in symbols. Paolo does not bicycle to school, or Roberto drives to school.

Let p = "Sally is three years old." Let q = "Sally's mom is thirty." Write the following statement in words. ∼q→p\sim q \rightarrow p∼q→p

Find the contrapositive of the statement. p→∼qp \rightarrow \sim qp→∼q A) ∼p→∼q\sim p \rightarrow \sim q∼p→∼q B) ∼q→p\sim q \rightarrow p∼q→p C) q→∼pq \rightarrow \sim pq→∼p D) ∼p→q\sim p \rightarrow q∼p→q

State whether the sentence is a statement or not. Close the door.

Write the converse of the conditional statement. I will buy a new computer if my laptop breaks.

Complete the following truth table. p q r (q\wedge\simr) (q\wedge\simr)\leftrightarrowp

Determine if the two statements are logically equivalent, negations, or neither. ∼p→q;∼p∨q\sim p \rightarrow q ; \sim p \vee q∼p→q;∼p∨q

Determine whether the following argument is valid, using the given forms of valid arguments and fallacies. \simp\veeq \simq \therefore\simp

Determine the validity of the following argument. q\rightarrow\simp

Write the contrapositive of the conditional statement. If I get a speeding ticket, my parents do not pay for my insurance.

Identify the statement as a conjunction, disjunction, conditional, or biconditional. We will build a pool if and only if we win the lottery.

Decide whether each statement is simple or compound. i. If you win the next round, you will be a finalist. ii. She is not feeling well. iii. 7+2=147 + 2 = 147+2=14 iv. He is taking history and economics.

Use a truth table to determine whether the argument is valid. p\wedgeq \simp\vee\simq \therefore\simp

Determine if the two statements are logically equivalent, negations, or neither. (p∨q)∧∼r;∼(p∧q)∨r( p \vee q ) \wedge \sim r ; \sim ( p \wedge q ) \vee r(p∨q)∧∼r;∼(p∧q)∨r

Is the following sentence a statement? Neither Ben nor Alonzo is going camping.

Use a truth table to determine whether the argument is valid. \simp\wedgeq

Problem Solving

Set

Numeration Systems

The Real Number System

Topics in Algebra

Consumer Mathematics

Measurement

Geometry

Probability and Counting Techniques

Statistics

Voting Methods

Graph Theory

Available Online: Other Mathematical Systems

Summary

Filters

Determine if the two statements are logically equivalent, negations, or neither. $p \rightarrow \sim q ; q \rightarrow \sim p$

Let p = "Sally is three years old." Let q = "Sally's mom is thirty." Write the following statement in words. $\sim q \rightarrow p$

Find the contrapositive of the statement. $p \rightarrow \sim q$ A) $\sim p \rightarrow \sim q$ B) $\sim q \rightarrow p$ C) $q \rightarrow \sim p$ D) $\sim p \rightarrow q$

Determine if the two statements are logically equivalent, negations, or neither. $\sim p \rightarrow q ; \sim p \vee q$

Decide whether each statement is simple or compound. i. If you win the next round, you will be a finalist. ii. She is not feeling well. iii. $7 + 2 = 14$ iv. He is taking history and economics.

Determine if the two statements are logically equivalent, negations, or neither. $( p \vee q ) \wedge \sim r ; \sim ( p \wedge q ) \vee r$