(A) If A then not(B) Negates to A and B. (B)- ?x?y A(x, y) Negates to ?x?y not(A

Question

(A) If A then not(B) Negates to A and B.

(B)- ?x?y A(x, y) Negates to ?x?y not(A(x, y))

(C)- If B then (If C then D) Negates to B and
Not(C) and not(D).

(D)- ?x?y A(x, y) Negates to ?x?y A(x, y)

(E)- A iff B Negates to (A and B) or (not(B) and
not(A))

(F)- ?!x?yB(x, y) Negates to ?!x?yB(x, y)

(G)- ?!x C(x) Negates to
?x notC(x) or
?x, y C(x) and C(y) implies x = y.

(H)- A implies (B or C) Negates to not(B) and
not(C) implies not(A).

(I)- A or B and C or D Negates to not(A) and
not(B) or not(C) and not(D).

(J)- (If A then B) iff (If C then D) Negates to
(A and not(B) and (If C then D)) or ((If A then
B) and C and not(D))

Explanation / Answer

(A) If A then not(B) Negates to A and B. Yes (B)- ?x?y A(x, y) Negates to ?x?y not(A(x, y)) F (C)- If B then (If C then D) Negates to B and Not(C) and not(D). Y (D)- ?x?y A(x, y) Negates to ?x?y A(x, y) YES (E)- A iff B Negates to (A and B) or (not(B) and fALSE not(A)) (F)- ?!x?yB(x, y) Negates to ?!x?yB(x, y) (G)- ?!x C(x) Negates to ?x notC(x) or ?x, y C(x) and C(y) implies x = y. yES (H)- A implies (B or C) Negates to not(B) and fALSE not(C) implies not(A). (I)- A or B and C or D Negates to not(A) and not(B) or not(C) and not(D). yES (J)- (If A then B) iff (If C then D) Negates to (A and not(B) and (If C then D)) or ((If A then fALSE B) and C and not(D))

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