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Which of the following is a definition of a proposition?

• A command that must be followed

• An exclamation that can be uttered

• A question that can be asked

• A sentence that may be asserted or denied

What is the truth value of the compound proposition p∨q⟺(p∧q)?

• Contradiction

• Tautology

• False

• True

Which of the following is the correct negation of the statement 'For every x∈U, P(x)'?

• There exists an x∈U such that not P(x)

• For every x∈U, not P(x)

• For every x∈U, P(x)

• There exists an x∈U such that P(x)

What does the statement '∀x∃yP(x,y)' mean?

• For every x and for all y the relation P(x,y) holds

• There is an x which stands to every y in the relation P(x,y)

• For every x there is a y such that P(x,y) holds

• There is an x and there is a y for which P(x,y) holds

If Px:x2+y2≥0 for all x and y, what is the quantified statement?

• ∃x∈E∃y∈O(x2+y2≥0)

• ∀x∈R∀y∈R(x-1+y-2≤2)

• ∃x∈E∃y∈O(x-1+y-2≤2)

• ∀x∈R∀y∈R(x2+y2≥0)

What is the correct translation of the statement '∀x(Q(x)⟹R(x))'?

• Some rationals are reals

• No rationals are reals

• Some rationals are not reals

• All rationals are reals

Which of the following is a property of a tautology?

• It is always true regardless of the truth values of its component propositions

• It is always false regardless of its component propositions

• It is sometimes true and sometimes false

• It is never true or false

What is the relationship between the existential and universal quantifiers?

• ∃xPx≡∀xP(x)

• ∀xPx≡∃xP(x)

• ∃xPx≡∃xP(x)

• ∀xPx≡∀xP(x)

Which method is used to describe sets by listing all the elements without repetition?

• Verbal Method

• Roster/Complete Listing Method

• Partial Listing Method

• Set-builder Method

What is the result of the operation A∪B if A = {2, 4, 6, 8, 9, 10} and B = {3, 5, 7, 9}?

• {2, 3, 4, 5, 6, 7, 8, 9, 10}

• {2, 4, 6, 8, 9, 10, 3, 5, 7}

• {2, 4, 6, 8, 9, 10, 3, 5, 7, 9}

• {2, 3, 4, 5, 6, 7, 8, 9, 10, 9}