Ch 2 Gateway

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Ch 2 Gateway

What is the contrapositive of the following statement?

If Joe goes fishing, then he needs bait.

A)	If he needs bait, then Joe goes fishing.
B)	If Joe goes fishing, then he does not need bait.
C)	If Joe does not go fishing, then he does not need bait.
D)	If he does not need bait, then Joe does not go fishing.

Consider the following statements.

p: The sum of two angles is 180°.
q: The two angles are supplements.

Which of the following is a symbolic representation of the statement:
“If sum of two angles is 180°, then the two angles are not supplements”?

Consider the following statements.

p: The sum of two angles is 180°.
q: The two angles are supplements.

Which of the following is a symbolic representation of the statement:
“If two angles are supplements, then the sum of two angles is not 180°”?

Consider the following arguments. If the first two statements are true, in which argument is the 3rd statement an incorrect conclusion?

A)	1 If we win the contest, then we will win the championship. 2 If we win the championship, then we will get a placque. 3 If we do not get a placque, then we did not win the contest.
B)	1 If John eats her beans, then she will get ice cream. 2 If John gets ice cream, then she will stay up late. 3 If John eats her beans, then she will stay up late.
C)	1 If Deanna studies, then she will pass the test. 2 If Deanna passes the test, then she will not be grounded. 3 If Deanna is grounded, then she will study.
D)	1 If it snows, then we will stay inside. 2 If we stay inside, then we will practice in the gym. 3 If it snows, then we will practice in the gym.

Which of the following statements represents a valid argument?

A)	If a > b and a > c, then c > b.	C)	If a < b and a < c, then b < c.
B)	If a < b and a < c, then a < b + c.	D)	If a < b and b < c, then a < c.

Which is the converse of the statement, If I am in Richmond, then I am in Virginia?

A)	If I am not in Virginia, then I am in Richmond.
B)	If I am not in Richmond, then I am not in Virginia.
C)	If I am not in Virginia, then I am not in Richmond.
D)	If I am in Virginia, then I am in Richmond.

Let z represent: Angle U is obtuse.
Let t represent: Angle K is obtuse.

Which is a symbolic representation of the following argument?
Angle U is obtuse if and only if Angle K is obtuse.
Angle U is obtuse or Angle K is obtuse.
Therefore, Angle U is obtuse and Angle K is obtuse.

Let a represent “x is an odd number”.
Let b represent “x is a multiple of 3”.

When x is 9, which of the following is true?

In which group of statements is the conclusion not justified by the previous pair of statements?

A)	All rangers work in the park. Sue is a ranger. Sue works in the park.	C)	All squares are rectangles. All rectangles are parallelograms. All squares are parallelograms.
B)	All fish live in the water. Some bugs live in the water. Some bugs are fish.	D)	All flying reptiles are extinct. A pteranodon is a flying reptile. All pteranodons are extinct.

10.

Consider the following statement.
If

, then x = 5.
Which is the converse of the statement?

A)	If , then .	C)	If , then .
B)	If , then .	D)	If , then .

11.

Which is the inverse of the statement below?
If you do your homework, then you will be prepared for the test.

A)	If you do your homework, then you will be prepared for the test.
B)	If you did not do your homework, then you will not be prepared for the test.
C)	If you are not prepared for the test, then you did not do your homework.
D)	If you are prepared for the test, then you did your homework.

12.

What is the converse of the following statement?

If the measure of an angle is 90º, then it is a right angle.

A)	If the measure of an angle is not 90º, then it is not a right angle.
B)	If the measure of an angle is not 90º, then it is a right angle.
C)	If it is a right angle, then the measure of an angle is 90º.
D)	If it is not a right angle, then the measure of an angle is not 90º.

13.

Which is the converse of the sentence, “If Tom leaves, then I will stay.”?

A)	If I do not stay, then Tom will not leave.
B)	If Tom leaves, then I will not stay.
C)	If I stay, then Tom will leave.
D)	If Tom does not leave, then I will not stay.

14.

Let p represent:
         Two angles are vertical angles.
Let q represent:
         The angles are congruent.

What is the symbolic representation of the following statement?
     If two angles are congruent, then the angles are vertical angles.

15.

If the conditional statement
“If you have a laptop, then you have a computer”
is represented by

, what is the symbolic representation of
“If you have a laptop, then you do not have a computer”?

16.

Let p represent                         x² = 17
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

17.

Which conclusion logically follows the true statements?

If negotiations fail, the hockey strike will not end.
If the hockey strike does not end, the Stanley Cup will not be played.

A)	If the hockey strike ends, the Stanley Cup will be played.
B)	If negotiations fail, the Stanley Cup will be played.
C)	If negotiations do not fail, the hockey strike will not end.
D)	If negotiations fail, the Stanley Cup will not be played.

18.

Which set of statements represents an invalid argument?

A)	If we do our chores, then we will go to the movies. If we go to the movies, then we will get some popcorn. If we do not get some popcorn, then we did not do our chores.
B)	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.
C)	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.
D)	If I work, then I will make money. If I make money, then I will buy clothes. If I work, then I will buy clothes.

19.

Which is a valid conclusion that can be drawn from these statements?

If a quadrilateral is a rectangle, then it is a parallelogram.
If a quadrilateral is a parallelogram, then its opposite sides are congruent.

A)	Every parallelogram is a rectangle.
B)	Opposite sides of a quadrilateral are congruent.
C)	Every quadrilateral is a rectangle.
D)	Opposite sides of a rectangle are congruent.

20.

If s

e, and e

z, then:

21.

Assuming these statements are true,

which of the following is a valid conclusion?	Some fish are egg-layers. All egg-layers like to nest.

A)	Some fish like to nest.
B)	Some egg-layers do not like to nest.
C)	All fish like to nest.
D)	All egg-layers are fish.

22.

Let p represent

and let q represent z is a rational number.

Which choice is a representation of the statement below?

If

= z, then z is not a rational number.

23.

Let p = An equation is of the form x² + y² = r².
Let q = Its graph is a circle.

Argument: If an equation is of the form x² + y² = r², then graph is a circle.
The graph is a circle.
Therefore, the equation is of the form x² + y² = r².

Which of the following is the symbolic representation of the given argument?

24.

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 parallelograms have angles. All squares have angles. Conclusion: All parallelograms are squares.
C)	Given: All squares have congruent angles. All rectangles have congruent angles. Conclusion: All rectangles are squares.
D)	Given: All four sided figures are quadrilaterals. All squares have four sides. Conclusion: All squares are quadrilaterals.

25.

Statement: If lines are skew, then they are not coplanar..

What is the inverse of the statement?

A)	If lines are not skew, then they are coplanar.
B)	If lines are coplanar, then they are not skew.
C)	If lines are skew, then they are coplanar.
D)	If lines are not coplanar, then they are skew.