Logic - Review Set A

What is the inverse of "If water is ice, then the water's temperature is 32^oF?"

• If water's temperature is 32 F, then it is ice.

• If water is not ice, then its temperature is not 32 F.

• If water's temperature is not 32 F, then it is not ice.

• Water is ice if an only if it is 32 F.

What is the converse of the following statement: If n is divisible by 10, then n is divisible by 5?

• If n is divisible by 5, then it is divisible by 10.

• If n is divisible by 10, then n is not divisible by 5.

• If n is divisible by 10, then it is an even number.

• If n is not divisible by 10, then n is not divisible by 5

Given p and r, which of the following is a symbolic representation of the statement "If today is not Thursday, then James is not wearing his purple vest?"

Consider the given statements. Assuming these statements are true, which is a valid conclusion?

• If Peter finishes his work, then he will rest.

• If Peter goes home, then he will rest.

• If Peter rests, then he will go home.

• If Peter rests, then he will finish his work.

Tags

CCSS.RI.8.1

CCSS.RI.8.8

CCSS.RL.11-12.1

CCSS.RL.8.1

CCSS.RL.9-10.1

• If it is thundering then we cannot swim.

• If we can swim, then it is thundering.

• If we cannot swim, then it is not thundering.

• If it is not thundering, then we can swim.

Which is a valid conclusion given the statement?

• Joe goes to a grocery store.

• Joe spends money

• Joe spends less than $100.

• Joe and his sister goes to the store.

Tags

CCSS.RI.11-12.2

CCSS.RI.9-10.1

CCSS.RL.11-12.1

CCSS.RL.8.1

CCSS.RL.9-10.1

Which type of reasoning allows the conclusion given the true statement?

• Law of Syllogism

• Law of Detachment

• Law of Contrapositive

• None

Which of the following statements are not true?

• If x = 4, then x² = 16

• If x ≠ 3, then x³ ≠ 27

• If x = 2, then x² = 4

• If x² = 4, then x = 2

Tags

CCSS.6.EE.B.5

Write the following as an if-then statement: "A group is a dozen if it has 12 objects."

• If a group does not have 12 objects, then it is not a dozen.

• If a group is not a dozen, then it does not have 12 objects.

• If a group has 12 objects, then it is a dozen.

• A group is a dozen if and only if it has 12 objects.