Discrete Math Final Exam Review: Logic

Which of the following conjunctions and disjunctions has a true truth value based on the statements below?

p: 5² = 25

q: There is water on Earth.

r: Milk is a fruit.

A true conditional is given below:

If two angles are complementary to the same angle, then the angles are congruent.

Which of the following uses the Law of Detachment to draw a valid conclusion?

Which of the following combinations of inputs for A, B, and C will create a false output for Y?

(False = 0, True = 1)

• A=0, B=1, C=0

• A=0, B=1, C=1

• A=1, B=0, C=0

• A=1, B=1, C=1

Which statement is true of the final column of the truth table?

• All of the truth values are true, making the final statement a tautology.

• Three of the truth values are true and one is false.

• Two of the truth values are true, and two are false.

• All of the truth values are false, making the final statement a contradiction.

If Haru drinks a truth serum, then he will tell the truth.

Which of the following is a valid conclusion based on the conditional statement above? (Assume the conditional statement, in this case, to be true.)

• Haru did not tell the truth. Therefore, he did not drink a truth serum.

• Haru drank a truth serum and did not tell the truth.

• Haru did not drink a truth serum. Therefore, he will not tell the truth.

• Haru told the truth. Therefore, he drank a truth serum.

When filled out correctly, how many of the inputs in the final column of the truth table will be true?

If Grandma gets out of her chair, then she'll make me a hot fudge sundae.

If Grandma makes me a hot fudge sundae, then I'm going to make a mess.

Using the Law of Syllogism, which of the following is a valid conclusion?

• If I make a mess, it's because Grandma made me a hot fudge sundae.

• If Grandma gets out of her chair, then I'm going to make a mess.

• If Grandma doesn't make me a hot fudge sundae, then I won't make a mess.

• If I make a mess, it's because Grandma got out of her chair.