Logic and Venn Diagrams

According to the Venn diagram below, which statement 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.

Let a be the statement: "It is raining outside."

Let b be the statement: "The football team will not practice outside today."

Which is the symbolic representation of the statement below?

It is raining outside and the football team will not practice outside today.

What is the converse of the statement below?

If you do your homework then you will be prepared for the test.

• If you are prepared for the test then you did your homework.

• If you are not prepared for the test then you did not do your homework.

• If you do your homework then you will be prepared for the test.

• If you do not do your homework then you will not be prepared for the test.

Given the statements: If a shape is a parallelogram, then opposite angles are congruent. A rhombus is a parallelogram. Which is a logical conclusion from the given statements?

• A rhombus has opposite angles that are congruent.

• The opposite sides of a rhombus are congruent.

• The diagonals of a rhombus are congruent.

• A rhombus is a quadrilateral.

Given the following argument: If it is not sunny on Saturday, Erin will not go to the beach. If Erin does not go to the beach, Erin will not play volleyball. Which of the following conclusions can be drawn?

• If it is not sunny on Saturday, Erin will go to the beach.

• If Erin does not go to the beach, then it is not sunny on Saturday.

• If it is not sunny on Saturday, Erin will not play volleyball.

• If it is sunny on Saturday, then Erin will play volleyball.

Which value for x is a counterexample for the following statement? For all positive values of x, x³ ≥ x.

• -1.0

• -0.1

• 0.1

• 1.0

Which statement below is the inverse of the following?

If two line segments have the same length, then they are congruent.

• If two line segments are not congruent, then they do not have the same length.

• If two line segments do not have the same length, then they are congruent.

• If two line serments do not have the same length, then they are not congruent.

• If two line segments are congruent, then they have the same length.

Which of the following would be a counterexample to the conditional statement below?

If a number is even, then it is double an odd number.

• 21

• 12

• 14

• 18

What is the inverse of the statement: "If I played video games for 8 hours, then my parents are not happy"?

• If my parents are not happy, then I played video games for 8 hours.

• If I did not play video games for 8 hours, then my parents are happy.

• If my parents are happy, then I did not play video games for 8 hours.

• If I played video games for 8 hours, then my parents are not happy.

What is the contrapositive of the statement: "If I played video games for 8 hours, then my parents are not happy"?

• If my parents are not happy, then I played video games for 8 hours.

• If I did not play video games for 8 hours, then my parents are happy.

• If my parents are happy, then I did not play video games for 8 hours.

• If I played video games for 8 hours, then my parents are not happy.