Logic - Review Set B

• If it is thundering, then it is raining.

• If it is not raining, then it is not thundering.

• If it is not thundering, then it is not raining.

• If it is thundering, then it is not raining.

Identify the contrapositive of the following statement.

• If two triangles are not both equilateral, then they are not similar.

• Two triangles are similar if and only if they are both equilateral.

• If two triangles are not similar, then they are not both equilateral.

• If two triangles are similar, then they are both equilateral.

Assume the following two statements are true. Which is a valid conclusion?

• If the dog runs loose, then you left the gate unlocked.

• If you did not leave the gate unlocked. Then the neighbors will not complain.

• If the neighbors complain, then you left the gate unlocked.

• If you left the gate unlocked, then the neighbors will complain.

Given the following conditional statement. Which of the following is the contrapositive?

• If it is not cold today, then I am not wearing an overcoat.

• If I am wearing an overcoat, then it is cold today.

• If I am not wearing an overcoat, then it is not cold today.

• If I am wearing an overcoat, then it is not cold today.

Assume the following two statements are true. Which is a valid conclusion?

• All cats are Persians.

• No cats have long hair.

• Some cats have long hair.

• All cats have long hair.

What is the converse of "If you are hungry, then you did not eat lunch?"

• If you did not eat lunch, then you are hungry.

• If you ate lunch, then you are not hungry.

• If you are not hungry, then you ate lunch.

• You are hungry if and only if you did not eat lunch.

What is the biconditional form of the statement: "If a whitetail deer has antlers, then it is a male deer?"

• A whitetail deer has no antlers if an only if it is not a male deer.

• A whitetail deer has antlers if and only if it is a male deer.

• If a whitetail deer has no antlers, then it is not a male deer.

• If a whitetail deer is male, then it has antlers.

Which of the following statements cannot be written as a true biconditional statement?

• If the sum of two angles is 90^o, then they are complementary.

• If two angles have the same measurement, then they are congruent.

• If 5x + 7 = 22, then x = 3.

• If two angles are a linear pair, then they are supplementary.

Which of the following represents the given statement in symbolic notation, given that 𝒑 represents “Kate is taking geometry” and 𝒒 represents “Kate takes an SOL test.”

• p ^ ~q

• p v ~q