Which connective in the following formula has the narrowest scope? Which has the widest? What does the negation have scope over? A ⟶ (B ∧ ¬(C ⟷ (D ∨ E)))

Form the negation of the following statements. Then apply De Morgan's law and/or conditional law, when applicable. Negation should appear only within predicates, i.e., no negation should be outside a quantifier or an expression involving logical connectives. Show all steps. a) Vx (P(x) A R(x)) b) Vy³z(-P(y)→→ Q(z)) c) 3x (P(x) V (VZ (R(z) →→Q(z))))

State whether the following claim is true or false and prove your answer. Claim: For any (non-empty) alphabet Σ, there is no language L ⊆ Σ∗ which is both regular and inherently ambiguous.

i need answer of all. if any answer will be skipped, your answer will be rejected. only complete answer will be accepted.   b) Make a truth table for the statement ¬P ∧ (Q → P). What can youconclude about P and Q if you know the statement is true? a) Make a truth table for the statement (P ∨ Q) → (P ∧ Q). c) Make a truth table for the statement ¬P → (Q ∧ R).