Interactive Lecture | Logical Equivalence

Multiple Choice

Which of the following best describes a tautology in propositional logic?

• A compound proposition that is always true, regardless of the truth values of its components.

• A compound proposition that is always false, regardless of the truth values of its components.

• A compound proposition that is sometimes true and sometimes false, depending on the truth values of its components.

• A proposition that cannot be determined.

Open Ended

Based on the examples and truth table, why is (p ∨ ¬p) considered a tautology and (p ∧ ¬p) considered a contradiction?

Fill in the Blanks

Fill in the blank: Compound propositions p and q are called logically equivalent if p ↔ q is a

.

Multiple Choice

Which of the following statements about logical equivalence is correct?

• p ≡ q means p and q are logically equivalent in all cases.

• p ≡ q is a logical connective.

• p ≡ q is a compound proposition.

• p ≡ q means p and q are always contradictions.

Multiple Choice

Which of the following is an application of tautologies or contradictions in computing?

• Ensuring that invariants are tautologies in program validation.

• Detecting unreachable code in debugging tools.

• Avoiding contradictory circuits in circuit design.

• All of the above.

Open Ended

Given the truth table, explain why p → q and ¬p ∨ q are logically equivalent.

Multiple Choice

Which law is demonstrated by the equivalence between p ∨ (q ∧ r) and (p ∨ q) ∧ (p ∨ r) as shown in the truth table?

• De Morgan's Law

• Distributive Law of Disjunction over Conjunction

• Commutative Law

• Idempotent Law

Multiple Choice

Which sequence of logical laws is used to show that ¬(p ∨ (¬p ∧ q)) ≡ (¬p ∧ ¬q)?

• Commutative, Associative, Absorption

• 2nd De Morgan’s, 1st De Morgan’s, Double Negation, Distributive, Negation, Commutative, Identity

• Distributive, Idempotent, Double Negation

• Absorption, De Morgan’s, Identity

Multiple Choice

Which of the following is a practical application of De Morgan's Laws?

• Sorting algorithms

• Database query design

• Graph coloring

• Binary search

Fill in the Blanks

The negation of the statement 'p ∨ q' using De Morgan's law is ___ p ∧ ___ q.

Multiple Choice

Which of the following statements is equivalent to the negation of 'Prada knows Java or Python' according to De Morgan's law?

• Prada does not know Java or Prada does not know Python.

• Prada knows Java or Prada knows Python.

• Prada does not know Java and Prada does not know Python.

• Prada knows Java and Prada knows Python.

Multiple Choice

According to De Morgan's law, what is the negation of the statement: 'Ralph will play Mobile Legends and Rianne will play Mobile Legends'?

• Ralph will not play Mobile Legends and Rianne will not play Mobile Legends.

• Ralph will play Mobile Legends and Rianne will play Mobile Legends.

• Ralph will not play Mobile Legends or Rianne will play Mobile Legends.

• Ralph will not play Mobile Legends or Rianne will not play Mobile Legends.

Open Ended

Negate the given statement using De Morgan’s Law:

Malec is happy and rich.

Open Ended

Negate the given statement using De Morgan’s Law:

Izza will study in Baguio or Laguna.

Open Ended

Negate the given statement using De Morgan’s Law:

Mika will study and exercise tomorrow.

Open Ended

Explain how De Morgan's law is applied to negate a conjunction, using the example 'Prada knows Java and Python.'

Open Ended

Negate the given statement using De Morgan’s Law:

Jeth will prepare dinner or watch a movie.

Open Ended

Negate the given statement using De Morgan’s Law:

Lorene will take IT and will practice programming.