20) (A B) [B (C D)] [A (B C)] (A D)
(¬A V B) [¬B V (C D)] ¬[¬A V (B C)] V (A D) { Law of Implies (PQ) = ¬PVQ }
(¬A V B) [¬B V (¬C VD)] ¬[¬A V (¬B VC)] V (¬A V D) { Law of Implies (PQ) = ¬PVQ }
(¬A V B) [¬B V (¬C VD)] [¬(¬A) ¬(¬B VC)] V (¬A V D) {By De Morgan's law ¬ (PVQ) = ¬P ¬Q}
(¬A V B) [¬B V (¬C VD)] [A (¬(¬B) ¬C)] V (¬A V D) {By De Morgan's law ¬ (¬A) = A}
(¬A V B) [¬B V (¬C VD)] [A (B ¬C)] V (¬A V D) {By De Morgan's law ¬ (¬B) = B}
[¬B V (¬C VD)] (¬A V B) [(B ¬C) A ] V (¬A V D) { Commutative law A B = B A }
[¬B V (¬C VD)] ¬A V (B B) ¬C (A V ¬A) V D {Associative law (A B) C = A (B C)}
[¬B V (D V ¬C)] ¬A V (B) ¬C (T) V D { we know that A V A = A }
[¬B V (D V ¬C)] ¬C ¬A V (B) (T) V D { Commutative law A V B = B V A }
¬B V D V (¬C ¬C) (B) V ¬A (T) V D {Associative law (A B) C = A (B C)}
¬B V D V (¬C) (B) V ¬A (T) V D { we know that ¬A ¬A = ¬A }
D V (¬C) V ¬B (B) V (¬A) (T) V D
D V (¬C) V (¬B B) V (¬A) (T) V D {Associative law (A V B) V C = A V (B V C)}
D V (¬C) V (F) V (¬A) (T) V D {We know that ¬A F = F}
(¬C) V (F) V (¬A) (T) V D V D { Commutative law A V B = B V A }
(¬C) V (F) V (¬A) (T) V (D V D)
(¬C) V (F) V (¬A) (T) V (D) {Associative law (A V A) = A }
(¬C) V (F) V (¬A) (T V D)
(¬C) V (F) V (¬A) (T) {We know that A V T = T}
(¬C) V (T) (F) V (¬A) { Commutative law A V B = B V A }
(¬C V T) (¬A) V (F) { Commutative law A V B = B V A }
(T) (¬A) V (F) {We know that ¬A V T = T}
(¬A) (T) V (F)
(¬A) (F) V (T) { Commutative law A V B = B V A }
(¬A F) V (T) {Associative law (A V B) V C = A V (B V C)}
(F) V (T) {We know that ¬A F = F}
T
The given Argument is Valid
20) (A B) [B (C D)] [A (B C)] (A D)
(¬A V B) [¬B V (C D)] ¬[¬A V (B C)] V (A D) { Law of Implies (PQ) = ¬PVQ }
(¬A V B) [¬B V (¬C VD)] ¬[¬A V (¬B VC)] V (¬A V D) { Law of Implies (PQ) = ¬PVQ }
(¬A V B) [¬B V (¬C VD)] [¬(¬A) ¬(¬B VC)] V (¬A V D) {By De Morgan's law ¬ (PVQ) = ¬P ¬Q}
(¬A V B) [¬B V (¬C VD)] [A (¬(¬B) ¬C)] V (¬A V D) {By De Morgan's law ¬ (¬A) = A}
(¬A V B) [¬B V (¬C VD)] [A (B ¬C)] V (¬A V D) {By De Morgan's law ¬ (¬B) = B}
[¬B V (¬C VD)] (¬A V B) [(B ¬C) A ] V (¬A V D) { Commutative law A B = B A }
[¬B V (¬C VD)] ¬A V (B B) ¬C (A V ¬A) V D {Associative law (A B) C = A (B C)}
[¬B V (D V ¬C)] ¬A V (B) ¬C (T) V D { we know that A V A = A }
[¬B V (D V ¬C)] ¬C ¬A V (B) (T) V D { Commutative law A V B = B V A }
¬B V D V (¬C ¬C) (B) V ¬A (T) V D {Associative law (A B) C = A (B C)}
¬B V D V (¬C) (B) V ¬A (T) V D { we know that ¬A ¬A = ¬A }
D V (¬C) V ¬B (B) V (¬A) (T) V D
D V (¬C) V (¬B B) V (¬A) (T) V D {Associative law (A V B) V C = A V (B V C)}
D V (¬C) V (F) V (¬A) (T) V D {We know that ¬A F = F}
(¬C) V (F) V (¬A) (T) V D V D { Commutative law A V B = B V A }
(¬C) V (F) V (¬A) (T) V (D V D)
(¬C) V (F) V (¬A) (T) V (D) {Associative law (A V A) = A }
(¬C) V (F) V (¬A) (T V D)
(¬C) V (F) V (¬A) (T) {We know that A V T = T}
(¬C) V (T) (F) V (¬A) { Commutative law A V B = B V A }
(¬C V T) (¬A) V (F) { Commutative law A V B = B V A }
(T) (¬A) V (F) {We know that ¬A V T = T}
(¬A) (T) V (F)
(¬A) (F) V (T) { Commutative law A V B = B V A }
(¬A F) V (T) {Associative law (A V B) V C = A V (B V C)}
(F) V (T) {We know that ¬A F = F}
T
The given Argument is Valid
I need help on the blue highlighted questions and 20 from the last picture. Our professor...