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Determine which of the following statements are negations in propositional logic notation with a tilde (~) as the main operator. Check all that apply.~[L ⊃ (~I • ~T)] ⊃ [~(X ⊃ ~O) ⋁ ~(Q ⊃ ~I)]~~[(V ⊃ Q) ⋁ (~H ⊃ P)]~~~{~(G ≡ ~~I) • ~~[~(X ≡ ~F) ⋁ ~(~A • H)]}~~(E ≡ X) ⊃ (H • ~V){[~K ⊃ (S ⋁ ~E)] • ~Z} • ~{(P ⊃ D) ⊃ L] ⊃ ~A}E • ~E~[(A • ~M) ⊃ (~W ⋁ A)]~(U ⊃ P)~{[(T ⋁ Q) ⊃ E] • [Y ⊃ (C ⋁ P)]}~[~(~Y • ~A) • (~X ⋁ ~L)] ⊃ ~~IDetermine which of the following statements are conjunctions in propositional logic with a dot (•) as the main operator. Check all that apply.~(C ≡ J) • ~(N ≡ Q)~(Q ⋁ H) • ~F~{~[~(B ⋁ N) ⊃ ~F] ≡ ~(U ⊃ M)} • H(A • ~K) ⋁ ~(E • ~V)~{~[~(~G ⋁ W) ⊃ ~Y] • (~~C ≡ ~Z)}[(D ⊃ L) • (C ⊃ X)] ⊃ [(O ⋁ Z) • ~K]~F • G(A • K) ≡ ~(~N ⋁ ~R){[(H ⋁ ~C) ⊃ ~Z] • [(~L ≡ ~K) ⊃ ~~V]} ≡ (B • I)~[(K ⊃ ~H) • (C ⊃ T)] • (X ≡ ~K)Determine which of the following statements are disjunctions in propositional logic with a wedge (⋁) as the main operator. Check all that apply.~{[~(T • ~E) ≡ (L • V)] ⋁ C} ⋁ {[Z ⊃ ~(A ≡ G)] ⋁ K}Q ⋁ [(A • V) • F][(~Z ⋁ ~H) ⋁ (C ⋁ O)] ≡ [(E ⋁ S) ⋁ (K ⋁ ~K)]~[(~N ⋁ ~C) ⋁ J] ⋁ [~V • ~(~U • ~Q)]{[W ⋁ (N• ~V)] ⋁ (F • Y)} ⊃ ~{~X ⋁ [(Z • ~N) ≡ O]}(R • E) ⋁ ~[F ≡ ~(M ⋁ O)]{[(X ⊃ V) ⊃ (O ⊃ N)] ⋁ [(U ⊃ Y) ⊃ (C ⊃ Q)]} ⊃ {[(B ⊃ G) ⋁ (N ⊃ M)] ⋁ F}W ⊃ [~(F • ~T) ⋁ ~(M • ~~C)]C ⋁ ~O~(O ⋁ R)Use your knowledge of propositional logic symbols and translation methods to determine which of the following statements are true. Check all that apply.The statement “Not both B and C” is equivalent to the statement “Either not B or not C.”Statements containing the words “not,” “it is false that,” or “it is not the case that” are usually best translated as negations with the tilde (~) operator.The statements ~(A • B) and ~A • ~B are equivalent according to De Morgan’s Rule.The horseshoe (⊃) operator expresses the logical function of material implication.In propositional logic, the fundamental elements are statements.The antecedent of a conditional represents a necessary condition.You should translate an ordinary language statement with the form “p only if q” into propositional logic notation as q ⊃ p.You should translate the statement “Today is Wednesday only if tomorrow if Thursday” into propositional logic notation as W ≡ T; where W stands for “Today is Wednesday,” and T stands for “Tomorrow is Thursday.”A dot (•) is the main operator in this statement: ~[(~Q ⋁ ~W) • (P ⊃ ~L)].The following expression is a well-formed formula (WFF): ~[(M ⋁ N) • (N ⋁ U)] ⋁ (X ⊃ Y).The tilde (~) is always placed in front of the statement it negates.A tilde (~) is the main operator in this statement: ~[(A • Z) ≡ ~(W • P)].You should translate an ordinary language statement with the form “p if q” into propositional logic notation as q ⊃ p.The tilde (~) operator is always placed between the two statements it connects.The triple bar (≡) operator expresses the logical relation of material implication.

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