Logic and Set Theory Quiz

Who was the first mathematician to make a serious study of symbolic logic?

• Gottfried Wilhelm Leibniz

• George Boole

• Augustus De Morgan

• David Hilbert

What is the basic building block of logic?

• Proposition

• Connective

• Variable

• Statement

Which of the following is NOT considered a proposition?

• Question

• Declarative sentence

• Opinion

• Command

What does De Morgan's Law for Negation state?

• p ↔ q ≡ ¬p ↔ ¬q

• ¬(p ∧ q) ≡ ¬p ∨ ¬q

• p ∨ q ≡ ¬p ∧ ¬q

• p → q ≡ ¬p ∨ q

What is the symbol for conjunction?

• ∨

• ∧

• →

• ↔

Which of the following statements is a tautology?

• ¬(A ∨ B)

• A → A

• A ∧ ¬A

• A ∨ ¬A

What is the definition of a null set?

• Set with repeated elements

• Set with one element

• Set with no elements

• Set with infinite elements

What is the cardinality of the set A = {2, 4, 6}?

• 2

• 3

• 4

• 5

Which of the following is a proper subset?

• A = {1, 2}, B = {1, 2, 3}

• A = {1, 2}, B = {2}

• A = {1, 2, 3}, B = {1, 2, 3}

• A = {1}, B = {1}

What is the symbol for the union of two sets?

• ∪

• ∩

• ⊂

• ⊆