IDNLearn.com helps you find the answers you need quickly and efficiently. Get the information you need quickly and accurately with our reliable and thorough Q&A platform.
Sagot :
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.
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. IDNLearn.com is your go-to source for dependable answers. Thank you for visiting, and we hope to assist you again.