Name:    SOL Topic #1: Logic

Multiple Choice
Identify the choice that best completes the statement or answers the question.

1.

Which is the inverse of the sentence, “If Sam leaves, then I will stay.”?
 a. If I stay, then Sam will leave. b. If Sam does not leave, then I will not stay. c. If Sam leaves, then I will not stay. d. If I do not stay, then Sam will not leave.

2.

According to the diagram, which of the following is true?
 a. All students in homeroom 234 belong to either the Math Club or the Science Club. b. All students in homeroom 234 belong to both the Math Club and the Science Club. c. No student in homeroom 234 belongs to both the Math Club and the Science Club. d. Some students in homeroom 234 belong to both the Math Club and the Science Club.

3.

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

When x is 7, which of the following is true?
 a. a b b. a ~b c. ~a b d. ~a ~b

4.

Which conclusion logically follows the true statements?

“If negotiations fail, the baseball strike will not end.”

“If the baseball strike does not end, the World Series will not be played.”
 a. If the baseball strike ends, the World Series will be played. b. If negotiations do not fail, the baseball strike will not end. c. If negotiations fail, the World Series will not be played. d. If negotiations fail, the World Series will be played.

5.

Which of the following groups of statements represents a valid argument?
 a. Given:  All quadrilaterals have four sides.            All squares have four sides.Conclusion:  All quadrilaterals are squares. b. Given:  All squares have congruent sides.            All rhombuses have congruent sides.Conclusion:  All rhombuses are squares. c. Given:  All four sided figures are quadrilaterals.            All parallelograms have four sides.Conclusion:  All parallelograms are quadrilaterals. d. Given:  All rectangles have angles.            All squares have angles.Conclusion:  All rectangles are squares.

6.

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 Richmond, then I am not in Virginia. c. If I am not in Virginia, then I am not in Richmond. d. If I am not in Virginia, then I am in Richmond.

7.

 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.

8.

 a. All happy people are musicians. b. All musicians like music. c. Some happy people do not like music. d. Some musicians like music.

9.

Consider the following arguements. If the first two statements are true, in which argument is the 3rd statement an incorrect conclusion?
 a. 1 If John studies, then he will pass the test.2 If John passes the test, then he will not be grounded.3 If John is grounded, then he will study. b. 1 If it rains, then we will stay inside.2 If we stay inside, then we will play games.3 If it rains, then we will play games. c. 1 If we win the game, then we will win the championship.2 If we win the championship, then we will get a trophy.3 If we do not get a trophy, then we did not win the game. d. 1 If Susan eats her broccoli, then she will get ice cream.2 If Susan gets ice cream, then she will stay up late.3 If Susan eats her brocoli, then she will stay up late.

10.

 a. No cat owners also own dogs. b. No dog owners also own fish. c. No fish owners also own cats. d. No pet owner owns more than one pet.

11.

 a. ~ q ® ~ p b. ~ p ® ~ q c. q ® p d. p ® q

12.

Let p represent

and let q represent
z is a rational number.
Which is a representation of the statement below?
If , then z is not a rational number.
 a. ~p ® ~q b. p ® q c. p ® ~q d. ~q ® ~p

13.

According to the Venn diagram, which statement is true?

 a. All isosceles triangles are also equilateral triangles. b. All equilateral triangles are also isosceles triangles. c. Some equilateral triangles are also isosceles triangles. d. No isosceles triangles are equilateral triangles

14.

Which of the following statements represents a valid argument?
 a. If a > b and a > c, then b > c. b. If a > b and b > c, then a > c. c. If a < b and a < c, then c < b. d. If a > b and a > c, then a > b + c.