probability

[Guest]

What is the difference between satisfiability and entailment? (Answer considering the
purpose and requirements of each). Determine which of the following are correct, and
explain your reasoning:
i. (P ∧Q) |= (P ⇐⇒ Q),
ii. P ⇐⇒ Q |= P ∨ Q
iii. X⇐⇒ Y |= ¬X ∨ Y
iv. (A ∧ B) =⇒ C |= (A =⇒ C) ∨ B =⇒ C)
v. Is (X ∨ Y) ∧ ¬(X =⇒ Y) satisfiable?
Explain the following proposition with examples: “Forward chaining is data-driven while backward chaining is goal-driven”.

[HallsofIvy]

What definitions of "satisfiability" and "entailment" are you using?