MAT1500 Week 3 Practice Test
Please use this to prepare for the Week 3 quiz. In this document, you will find:
Practice problems
Solutions
Common errors
Please don’t miss any of these sections. Taking the time now to prepare will help you do your very
best on the quiz. Please be sure to show your work for every problem that requires it. Full credit
cannot be awarded when work is missing.
#1 Consider the following simple statements:
p: It is time for dinner.
q: I will read my book.
Consider the compound statements and write each statement in symbolic form:
a. It is time for dinner or I will read my book.
b. If it is time for dinner, then I will read my book.
c. I will read my book and it is time for dinner.
#2 Consider the compound statements below:
a. Our meeting is postponed and we will meet if the power comes back on.
b. It is not true that our meeting is postponed and the power comes back on, or we will meet.
Give simple statements p, q, and r and give the symbolic statement that best represents the
compound statement.
Is the compound statement a negation, conjunction, disjunction, conditional, or biconditional?
#3 Consider the following simple statements:
p: The house is painted white.
q: The fence is broken.
r: It is sunny outside.
Write the following symbolic statements in words.
a. r ↔ (p ˅ q)
b. (p ^ q) ↔ r
c. q ^ (r ↔ p)
,#4 Consider the statement:
~p ˄ (q ˄ ~r)
Determine if this statement is true or false in each of the following cases:
a. p is true, q is false, and r is true.
b. p is false, q is true, and r is false.
#5 Consider the following simple statements:
p: I cook dinner.
q: I make coffee.
r: The family is happy.
Consider the compound statement:
I cook dinner and make coffee, or the family is not happy.
Write the statement in symbolic form.
Construct a truth table for this symbolic statement.
#6 Consider the following compound statement:
If 12 = 4, then 32 = 9
Consider the simple statements:
p: 12 = 4
q: 32 = 9
Determine the truth value for the simple statements.
Determine the truth value for the compound statement.
#7 Consider the information in the chart below:
, Using the information provided above, consider the compound statements below:
a. Pit Bulls have the highest percentage of bites to population ratio if and only if German
Shepherds have a percentage greater than 0.002 and Chows have a percentage less than 0.004.
b. Rottweilers have the highest percentage of bites to population ratio if and only if Pit Bulls have
the lowest percentage of bites to population ratio or German Shepherds have a percentage less
than 0.002.
Give the simple statements p, q, and r, and determine their truth values.
Determine if the compound statements are true or false.
#8 Consider the following statements:
p→q and ~p → ~q
Use truth tables to determine if the statements are equivalent.
#9 Consider the following statements:
a. It is false that the sun is not shining or the grass is not green.
b. The sun is not shining and the grass is green.
Use De Morgan’s laws to write equivalent statements.
#10 Consider the following statement:
If you study your homework, then you will make a good grade on the test.
Write the converse, inverse, and contrapositive of this statement.
Please use this to prepare for the Week 3 quiz. In this document, you will find:
Practice problems
Solutions
Common errors
Please don’t miss any of these sections. Taking the time now to prepare will help you do your very
best on the quiz. Please be sure to show your work for every problem that requires it. Full credit
cannot be awarded when work is missing.
#1 Consider the following simple statements:
p: It is time for dinner.
q: I will read my book.
Consider the compound statements and write each statement in symbolic form:
a. It is time for dinner or I will read my book.
b. If it is time for dinner, then I will read my book.
c. I will read my book and it is time for dinner.
#2 Consider the compound statements below:
a. Our meeting is postponed and we will meet if the power comes back on.
b. It is not true that our meeting is postponed and the power comes back on, or we will meet.
Give simple statements p, q, and r and give the symbolic statement that best represents the
compound statement.
Is the compound statement a negation, conjunction, disjunction, conditional, or biconditional?
#3 Consider the following simple statements:
p: The house is painted white.
q: The fence is broken.
r: It is sunny outside.
Write the following symbolic statements in words.
a. r ↔ (p ˅ q)
b. (p ^ q) ↔ r
c. q ^ (r ↔ p)
,#4 Consider the statement:
~p ˄ (q ˄ ~r)
Determine if this statement is true or false in each of the following cases:
a. p is true, q is false, and r is true.
b. p is false, q is true, and r is false.
#5 Consider the following simple statements:
p: I cook dinner.
q: I make coffee.
r: The family is happy.
Consider the compound statement:
I cook dinner and make coffee, or the family is not happy.
Write the statement in symbolic form.
Construct a truth table for this symbolic statement.
#6 Consider the following compound statement:
If 12 = 4, then 32 = 9
Consider the simple statements:
p: 12 = 4
q: 32 = 9
Determine the truth value for the simple statements.
Determine the truth value for the compound statement.
#7 Consider the information in the chart below:
, Using the information provided above, consider the compound statements below:
a. Pit Bulls have the highest percentage of bites to population ratio if and only if German
Shepherds have a percentage greater than 0.002 and Chows have a percentage less than 0.004.
b. Rottweilers have the highest percentage of bites to population ratio if and only if Pit Bulls have
the lowest percentage of bites to population ratio or German Shepherds have a percentage less
than 0.002.
Give the simple statements p, q, and r, and determine their truth values.
Determine if the compound statements are true or false.
#8 Consider the following statements:
p→q and ~p → ~q
Use truth tables to determine if the statements are equivalent.
#9 Consider the following statements:
a. It is false that the sun is not shining or the grass is not green.
b. The sun is not shining and the grass is green.
Use De Morgan’s laws to write equivalent statements.
#10 Consider the following statement:
If you study your homework, then you will make a good grade on the test.
Write the converse, inverse, and contrapositive of this statement.
