Question 1 Write
a negation for the statement.
Charlie plays football.
Question options:
Charlie
does not like football.
Not Charlie
plays football.
Charlie does not play football.
Charlie
plays basketball.
Question 2 Write
a negation for the statement.
My brother is asleep.
Question options:
My sister
is awake.
My brother is not asleep.
My sister
is asleep.
The person
who is asleep is not my brother.
Question 3 Write
a negation for the statement.
That athlete wants to be a musician.
Question options:
That
musician wants to be an athlete.
That
musician does not want to be an athlete.
That athlete does not want to be
a musician.
That
athlete is not a musician.
Question 4 Translate
the symbolic compound statement into words.
Let p represent the statement "Her name is Lisa"
and let q represent the statement "She lives in Chicago."
p ^ q
Question options:
Her name is
Lisa and she doesn't live in Chicago.
Her name is
Lisa or she lives in Chicago.
Her name is Lisa and she lives
in Chicago.
If her name
is Lisa, she lives in Chicago.
Question 5 Let p
represent the statement, "Jim plays football", and let q represent
"Michael plays basketball". Convert the compound statements into
symbols.
Jim does not play football and Michael does not play
basketball.
Question options:
~p V ~q
~p ^ ~q
p V q
p ^ q
Correct
answer is B
Question 6 Let p
represent the statement, "Jim plays football", and let q represent
"Michael plays basketball". Convert the compound statements into
symbols.
Jim does not play football and Michael plays basketball.
Question options:
p ^ q
~(p ^ q)
~p ^ q
~p V q
Correct
answer is C
Question 7 Construct
a truth table for the statement.
~p ^ ~q
Question options:
Correct answer is D
Question 8 Construct
a truth table for the statement.
(p ^ ~q) ^ t
Question options:
Correct answer is B
Question 9 Construct a truth table for the statement.
(t ^ p) V (~t ^ ~p)
Question options:
Correct
answer is D
Question 10 Write a
negation of the statement.
No fifth graders play soccer.
Question options:
Everybody
does not play soccer.
Everybody
plays soccer.
Some fifth graders play soccer.
Fifth
graders play soccer.
Question 11 Write a
negation of the statement.
Some people don't like walking.
Question options:
Nobody
likes walking.
Some people
like walking.
All people like walking.
Some people
don't like driving.
Question 12 Write
the compound statement in symbols.
Let r = "The food is good," p = "I eat too
much," q = "I'll exercise."
If the food is good and if I eat too much, then I'll
exercise.
Question options:
Correct
answer is C
Question 1 Write
the statement as an equivalent statement that does not use the if . . . then
connective. Remember that p → q is equivalent to ~p q.
If the sun comes out Tuesday, the roses will open.
The sun comes out Tuesday and the roses will not open.
The sun does not come out Tuesday or the roses will not
open.
The sun does not come out Tuesday and the roses will not
open.
The sun
does not come out Tuesday or the roses will open.
Question 2 Write
the indicated statement. Use De Morgan’s Laws if necessary.
If I pass, I'll party.
Contrapositive
If I don't
pass, I won't party.
If I party,
then I passed.
I'll party
if I pass.
If I don't party, I didn't pass.
Question 3 Write
the indicated statement. Use De Morgan’s Laws if necessary.
If you like me, then I like you.
Converse
If I like you, then you like me.
I like you
if you don't like me.
If you
don't like me, I don't like you.
I don't
like you if you don't like me.
Question 4 Write
the indicated statement. Use De Morgan’s Laws if necessary.
If it is love, then it is blind.
Contrapositive
If it is
blind then it is love.
If it is
blind then it is not love.
It is blind
if it is love.
If it is not blind, then it is
not love.
Question 5 Write
the indicated statement. Use De Morgan’s Laws if necessary.
If the moon is out, then we will start a campfire and we
will roast marshmallows.
Inverse
Question options:
If the moon
is not out, then we will start a campfire but we will not roast marshmallows.
If the moon is not out, then we
will not start a campfire or we will not roast marshmallows.
If we do
not start a campfire or we do not roast marshmallows, then the moon is not out.
If we start
a campfire and we roast marshmallows, then the moon is out.
Question 6 Write
the indicated statement. Use De Morgan’s Laws if necessary.
If the chores are done, then we will go to the carnival and
we will eat cotton candy.
Contrapositive
Question options:
If we do not go to the carnival
or we do not eat cotton candy, then the chores are not done.
If the
chores are not done, then we will not go to the carnival or we will not eat
cotton candy.
If we go to
the carnival and we eat cotton candy, then the chores are done.
If we do
not go to the carnival and we do not eat cotton candy, then the chores are not
done.
Question 7 Use
one of De Morgan's laws to write the negation of the statement.
10 + 2 = 12 and 8 - 3 ≠ 5
Question options:
10 + 2 ≠ 12
and 8 - 3 = 5
10 + 2 = 12
and 8 - 3 = 5
10 + 2 = 12
or 8 - 3 ≠ 5
10 + 2 ≠ 12 or 8 - 3 = 5
Question 8 Use a
truth table to decide if the two statements are equivalent.
~p ~q; ~(p q)
Question options:
True
False
Question 9 Use a
truth table to decide if the two statements are equivalent.
~q p; ~q → p
Question options:
True
False
Question 10 Use a
truth table to decide if the two statements are equivalent.
q → p; p → q
Question options:
True
False
1.
All fish can dream. Any dead animal is unable to
dream. All live animals have a heartbeat.
a)
Any dead animal has no heartbeat.
b)
All live animals can dream.
c) All fish have a heartbeat.
d)
Any dead fish can dream.
2.
Use the premises to give a conclusion that
yields a valid argument.
If you pay taxes, then you are a
good citizen. People who do not pay taxes do not receive a tax bill. If it is
April, then Mark receives a tax bill.
a)
Mark did not receive a tax bill.
b)
Mark is not a good citizen.
c) Mark is a good citizen.
d)
Mark did not pay taxes.
3.
Use the premises to give a conclusion that
yields a valid argument:
Students who watch television
while doing homework lower their grades. Students who lower their grades get
grounded. Grounded people will not be allowed to watch television.
a) Students who watch television
while doing homework will not be allowed to watch television.
b)
Students who are grounded watch television while
doing homework.
c)
Students who watch television will be grounded.
d)
Students who watch television will not be
allowed to watch television.
4.
Write the statement symbolically.
Some lights are green.
A) ∀x [l(x) → g(x)]
B) ∀x [l(x) ∧ g(x)]
C) ∃x [l(x) ∧ g(x)]
D) ∃x [l(x) → g(x)]
5.
Write the statement symbolically.
All refrigerators are appliances.
A) ∀x [r(x) ∧ a(x)]
B) ∃x [r(x) ∧ a(x)]
C) ∃x [r(x) → a(x)]
D) ∀x [r(x) → a(x)]
6.
Write the statement symbolically.
No dogs can read.
A) ∀x [d(x) → ~r(x)]
B) ∀x [~d(x) ∧ r(x)]
C) ∀x [d(x) ∧ ~r(x)]
D) ∀x [~d(x) → r(x)]
7.
Write the statement symbolically.
Some cats can sing.
A) ∀x [c(x) ∧ s(x)]
B) ∃x [c(x) ∧ s(x)]
C) ∃x [c(x) ∨ s(x)]
D) ∀x [c(x) ∨ s(x)]
8.
Write the negative of the statement.
∀x [g(x) → c(x)
A) ∃x [g(x) ∧ ~c(x)]
B) ∀x [c(x) → g(x)]
C) ∀x [g(x) → ~c(x)]
D) ∃x [g(x) ∨ ~c(x)]
9.
Write the negative of the statement.
∃x [m(x) ∧ n(x)]
A) ∃x [m(x) → ~n(x)]
B) ∃x [~m(x) → n(x)]
C) ∀x [~m(x) → n(x)]
D) ∀x [m(x) → ~n(x)]
10. Determine
if the argument is valid.
All business
expenses are covered by the company.
____________________________________________
This expense is
a business expense.
a)
Invalid b) Valid
11. Determine
if the argument is valid.
All businesses
are subject to safety inspections.
___________________________
This restaurant
is a business.
a)
Invalid b)Valid
12. Determine
if the argument is valid.
All astronauts
are healthy.
______________________
Lawrence is not
healthy.
a)
Valid b) Invalid
13. Determine
if the argument is valid.
All businessmen
wear suits.
________________________
Aaron wears a
suit.
a)
Valid b) Invalid
14. The
argument has a true conclusion. Identify the argument as valid or invalid.
Eric is older
than Camille.
_____________________
Todd is younger
than Eric.
a)
Invalid b) Valid
15. The
argument has a true conclusion. Identify the argument as valid or invalid.
A square is a
parallelogram.
______________________
A square has
four sides.
a) Invalid b)
Valid
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