Answered

Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Get immediate and reliable solutions to your questions from a community of experienced experts on our Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

Which of the following is a tautology?

a. p → p
b. p ∨ p
c. p ∧ T
d. P ∨ ⇁p

Sagot :

wwwahemaddani86

Answer:

d.(p ∧ ¬p) .

Step-by-step explanation:

A tautology in logic is a formula or assertion that is true in every possible interpretation. This means that the statement is always true, regardless of the truth values of its variables.

Let's evaluate each of the given statements:

a.) ¬(p ∧ q) → ¬(p ∨ q)

b.) (p ∧ ¬p) ↔ (q ∨ ¬q)

c.) (p ∧ ¬p) → ¬(q ∨ ¬q)

d.) (p ↔ ¬p) ∧ (q ∨ ¬q)

Evaluation

a.) ¬(p ∧ q) → ¬(p ∨ q)

This is not a tautology. There are cases where this statement can be false. For example, if p is true and q is false, then ¬(p ∧ q) is true, but ¬(p ∨ q) is false.

b.) (p ∧ ¬p) ↔ (q ∨ ¬q)

This is a tautology. The left side (p ∧ ¬p) is a contradiction and is always false. The right side (q ∨ ¬q) is a tautology and is always true. A false statement is equivalent to a true statement in logic, so this entire statement is always true.

c.) (p ∧ ¬p) → ¬(q ∨ ¬q)

This is not a tautology. The left side (p ∧ ¬p) is a contradiction and is always false. The right side ¬(q ∨ ¬q) is a contradiction and is always false. A false statement implies a false statement is not always true.

d.) (p ↔ ¬p) ∧ (q ∨ ¬q)

This is not a tautology. The left side (p ↔ ¬p) is a contradiction and is always false. The right side (q ∨ ¬q) is a tautology and is always true. A false statement and a true statement is not always true.

We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.