Discrete Mathematics Quiz

Which of the following is a subset of {1, 2, 3}?

• {1, 2, 3, 4}

• {2, 3}

• {0}

• {4, 5}

What is the power set of {a, b}?

• {{a}, {b}}

• {a, b, {a, b}}

• {{}, {a}, {b}, {a, b}}

• {a, b}

The union of {1, 2} and {2, 3} is:

• {1, 2, 3}

• {2}

• {1, 3}

• {1, 2}

The intersection of {1, 2, 3} and {2, 3, 4} is:

• {1, 4}

• {2, 3}

• {1, 2, 3, 4}

• {2}

Which of the following is a tautology?

• p ∧ ¬p

• p ∨ ¬p

• p → q

• ¬(p ∨ q)

Which rule of inference is used in the argument: "If it rains, the ground is wet. It rains. Therefore, the ground is wet."?

• Modus Tollens

• Modus Ponens

• Hypothetical Syllogism

• Disjunctive Syllogism

Which is the contrapositive of "If it is sunny, I will go for a walk"?

• If I go for a walk, then it is sunny

• If it is not sunny, I will not go for a walk

• If I do not go for a walk, it is not sunny

• If it is sunny, I will not go for a walk

What is the negation of "For all x, P(x) holds"?

• For all x, ¬P(x)

• There exists x such that ¬P(x)

• There exists x such that P(x)

• None of the above

Which is a valid statement?

• ∀x ∈ ℝ, x² ≥ 0

• ∀x ∈ ℝ, x² < 0

• ∃x ∈ ℝ, x² < 0

• ∃x ∈ ℝ, x² < -1

Direct proof is best used when:

• Proving ¬P → ¬Q

• Proving P → Q

• Proving by contradiction

• Proving the existence of an element