MATH 101

What is the symbolic representation for the statement "It is not sunny"?

• p AND q

• p OR q

• NOT p

• p XOR q

Apply De Morgan's Laws to simplify the statement: "It is not the case that either I'm hungry or I'm tired."

• I'm not hungry and I'm not tired.

• I'm hungry and I'm tired.

• I'm not hungry or I'm not tired.

• I'm hungry or I'm tired.

Is the statement "It is both raining and not raining" a tautology or a contradiction?

• Contradiction

• Tautology

• Both

• Neither

Determine the validity of the following syllogism:

• "All dogs have tails."

• "Rover has a tail."

• "Therefore, Rover is a dog."

• Valid

• Invalid

• Cannot be determined

• Neither Valid nor Invalid

Determine if the statement "If I pass the exam, then I studied" logically implies "If I didn't study, then I won't pass the exam." Explain your answer.

• It implies

• It doesn't imply

• Cannot be determined

• Neither True nor False

What is the contrapositive of the statement "If it's a holiday, then the office is closed"?

• If it's a holiday, then the office is open.

• If the office is closed, then it's a holiday.

• If it's not a holiday, then the office is open.

• If the office is open, then it's not a holiday.

Determine whether the statement "If it is Monday, then I have a meeting" is equivalent to "If I don't have a meeting, then it's not Monday."

• They are equivalent

• They are not equivalent

• Cannot be determined

• Neither True nor False

Given the truth values p = True and q = False, what is the truth value of the compound proposition "p OR q"?

• True

• False

• Cannot be determined

• Neither True nor False

Construct a truth table for the compound proposition "p AND (q OR NOT r)." What is the value of the proposition when p = True, q = True, and r = False?

• True

• False

• Cannot be determined

• Neither True nor False

Which of the following pairs of statements are logically equivalent?

• "It is raining" and "It is not raining"

• "It is sunny" and "It is warm"

• "It is snowing" and "It is cold"

• "It is daytime" and "It is nighttime"