Discrete Structures (Test 1)

In Boolean algebra, which of the following statements is always true?

• A AND B = A OR B
  

• A OR 0 = A

• A AND 1 = 0

• A OR A' = 0

Which of the following is a Tautology?

• P∧¬P

• P∨¬P

• P∧Q

• P⟹Q∧¬Q

A proposition that is always false is called:

• Tautology

• Contingency

• Contradiction

• Predicate

What is the truth value of the compound statement (P∨Q)∧(¬P∨R) when P is true, Q is false, and R is true?

• True

• False

• Undefined

• Cannot be determined

Which of the following logical gates outputs true only when both inputs are true?

• OR

• AND

• NOT

• NAND

Which of the following statements is a predicate?

• x+2=5

• P∨Q

• ∀x(x>0)

• P∧Q

Which of the following is a correct statement about a truth table?

• It can only contain two columns.

• It cannot represent compound statements.

• It shows the relationships between inputs and outputs of a logical expression.

• It is not useful in digital logic design.

The expression P∨Q is false when:

• Both P and Q are true

• P is true and Q is false

• Both P and Q are false
  

• P is false and Q is true

If P is true and Q is false, what is the value of P∧(P∨Q)?

• True

• False

• Undefined

• Cannot be determined

What is the negation of the statement "All birds can fly"?

• Some birds cannot fly.

• No birds can fly.

• Not all birds can fly.

• All birds cannot fly.