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1.
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Which is the converse of the sentence, “If Ted leaves, then I will
stay.”?
A) | If I do not stay, then Ted will not leave. | B) | If I stay, then Ted
will leave. | C) | If Ted leaves, then I will not stay. | D) | If Ted does not leave, then I will not
stay. |
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2.
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Which conclusion logically follows the true
statements?
If negotiations fail, the soccer
strike will not end.
If the soccer strike does not end,
the World Cup will not be played.
A) | If the soccer strike ends, the World Cup will be played. | B) | If negotiations do
not fail, the soccer strike will not end. | C) | If negotiations fail, the World Cup will not be
played. | D) | If negotiations fail, the World Cup will be played. |
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3.
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Let a represent “x is an even number”.
Let b
represent “x is a multiple of 3”.
When x is 9, which of the
following is true?
A) | a ^ b | B) | ~a ^ b | C) | ~a ^ ~b | D) | a ^
~b |
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4.
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Which of the following groups of statements represents a valid
argument?
A) | Given: All quadrilaterals have four
sides.
All kites have four
sides.
Conclusion: All quadrilaterals are kites. | B) | Given: All
squares have congruent angles.
All rectangles have congruent angles.
Conclusion: All rectangles are
squares. | C) | Given: All four sided figures are
quadrilaterals.
All
parallelograms have four sides.
Conclusion: All parallelograms are
quadrilaterals. | D) | Given: All kites have
sides.
All squares have
sides.
Conclusion: All kites are squares. |
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5.
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Which is the contrapositive of the statement, If I am in Richmond, then I
am in Virginia?
A) | If I am in Virginia, then I am in Richmond. | B) | If I am not in
Virginia, then I am not in Richmond. | C) | If I am not in Virginia, then I am in
Richmond. | D) | If I am not in Richmond, then I am not in Virginia. |
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6.
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According to the Venn diagram, | which is true? |  | | |
A) | All football players play offense or defense. | B) | No football players
play offense and defense. | C) | All football players play
defense. | D) | Some football players play offense and defense. |
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7.
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Assuming these statements are true, Some fish are live-bearers.
All live-bearers like to
nurse.
which of the following is a valid conclusion?
A) | All live-bearers are fish. | B) | All fish like to nurse. | C) | Some live-bearers do
not like to nurse. | D) | Some fish like to
nurse. |
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8.
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Consider the following statements.
p: The sum of two angles is
90°.
q: The two angles are complements.
Which of the following is a symbolic
representation of the statement:
“If two angles are
not complements, then the sum of two angles is not 90°”?
A) | ~q ® ~p | B) | q ®
~p | C) | ~q ® p | D) | p ®
~q |
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9.
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Let p
represent
 and let q
represent
z is a rational number.
Which choice is a representation of the statement
below?
If  ¹ z, then z is not
a rational number.
A) | ~p ® ~q | B) | p ®
q | C) | p
® ~q | D) | ~p ®
q |
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10.
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According to the Venn diagram, |
which statement is true? |  | | |
A) | All polygons are also pentagons. | B) | All pentagons are also
polygons. | C) | Some pentagons are also polygons. | D) | No polygons are
pentagons. |
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11.
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Which of the following statements represents a valid argument?
A) | If a < b and a < c, then b <
c. | C) | If a > b and a > c, then c >
b. | B) | If a < b and b < c, then a <
c. | D) | If a <
b and a < c, then a < b +
c. |
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12.
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According to the Venn diagram above, which is true?  A) | All trucks have Manual transmissions and All-Wheel drive. | B) | No trucks have
4-Cylinder and All-Wheel drive. | C) | All trucks have All-Wheel
drive. | D) | Some trucks have Manual transmissions and 4-Cylinders.
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13.
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Which is the contrapositive of the statement below?
If you do your
homework, then you will be prepared for the test.
A) | If you did not do your homework, then you will not be prepared for the
test. | B) | If you are prepared for the test, then you did your homework. | C) | If you do your
homework, then you will be prepared for the test. | D) | If you are not prepared for the test, then you
did not do your homework. |
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14.
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Which set of statements represents an invalid argument?
A) | If I do my homework, then I will get a good quiz grade.
If I get a good quiz
grade, then I will get a homework pass.
If I do my homework, then I will get a homework
pass. | B) | If we clean up our room, then we will go to the mall.
If we go to the mall, then
we will get some new clothes.
If we do not get some new clothes, then we did not clean up our
room. | C) | If Bill goes to his grandparents, then he will go go 4-wheeling.
If Bill goes go
4-wheeling, then he will buy gas.
If Bill does not buy gas, then he will go to his grandparents.
| D) | If it is your 16th birthday, then you can get your license.
If you can get your
license, then you might get a car.
If it is your 16th birthday, then you might get a car.
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15.
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Statement: If lines are skew, then they
are not coplanar..
What is the contrapositive of the statement?
A) | If lines are not coplanar, then they are skew. | B) | If lines are
coplanar, then they are not skew. | C) | If lines are skew, then they are
coplanar. | D) | If lines are not skew, then they are coplanar. |
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16.
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In the Venn diagram, Q represents
the set of all quadrilaterals,
P represents the set of all parallelograms,
and
R represents the set of all rectangles.
Based on the diagram, which is a valid
conclusion? |  | | |
A) | All rectangles are parallelograms. | B) | All parallelograms are
rectangles. | C) | Some rectangles are not parallelograms. | D) | No rectangles are
parallelograms. |
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17.
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What is the inverse of the following statement?
If Joe goes fishing,
then he needs bait.
A) | If Joe does not go fishing, then he does not need bait. | B) | If he does not need
bait, then Joe does not go fishing. | C) | If he needs bait, then Joe goes
fishing. | D) | If Joe goes fishing, then he does not need bait. |
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18.
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In which group of statements is the conclusion not justified by the
previous pair of statements?
A) | All teachers work in the school.
Mary is a teacher.
Mary works in the
school. | C) | All squares are rhombi.
All rhombi are parallelograms.
All squares are
parallelograms. | B) | All dinosaurs are extinct.
A triceratop is a dinosaur.
All triceratops are
extinct. | D) | All fish live in
the water.
Some snakes live in the water.
Some snakes are fish. |
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19.
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Let p
represent
x2 = 16
and let q
represent
x is not a whole number.
Which is a representation of the statement
below?
If x is not a whole number, then x2 ¹ 16.
A) | q ® ~p | B) | ~q ® ~p | C) | ~q ® p | D) | q ® p |
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20.
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According to the diagram, | which is true? |  | | |
A) | No acute triangles are isocseles. | C) | Some equilateral triangles are not
isocseles. | B) | No equilateral triangles are acute. | D) | Some isocseles triangles are
acute. |
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21.
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Consider the following
statement.
If 4x =
12, then x = 3.
Which is the inverse of the
statement?
A) | If x ¹ 3, then 4x ¹
12 | C) | If x = 3, then 4x =
12 | B) | If 4x ¹ 12, then x ¹
3. | D) | If x = 3, then 4x ¹
12 |
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22.
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Let p = An equation is of the form  . Let q =
Its graph is a line. Argument: If an equation is of
the form  , then its graph is a
line. The graph is not a
line.
Therefore, the equation is not of the form  . Which of the following is the symbolic
representation of the given argument?
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23.
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Which Venn diagram represents all the following set of statements?
· Some quadrilaterals are parallelogram.
· Some quadrilaterals are trapezoid.
· No quadrilateral is both parallelogram and
trapezoid.
· Some parallelograms are
rhombii.
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24.
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Which of the following statements
| must be true
about this Venn diagram? |  | | |
A) | All rectangles are rhombi. | B) | Some rhombi are rectangles. | C) | Quadrilaterals are not rhombi or rectangles. | D) | All quadrilaterals are rhombi and
rectangles. |
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25.
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If the conditional statement
“If
you have a MP3 player, then you have music”
is represented by p ® q, what is the symbolic representation
of
“If you do not have music, then you do not have a
MP3 player”?
A) | ~q ® ~p | B) | q ®
~p | C) | ~q ® p | D) | p ®
~q |
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