1) Which of the following are correct applications of the rule cited? [0.1 mark each]

a. ~ (A . B) Ú ~ (C . D) / ~ ((A . B) . (C . D)) DeM.

b. ~ ~ B ⊃ ~ ~ A / ~ ~ A ⊃ ~ ~ B Contrap.

c. ~ (~ A ⊃ B) ⊃ (B Ú ~ A) / ~ (A Ú B) Ú (B Ú ~ A) C.E.

d. (A ⊃ B) ⊃ (C ⊃ (D . F)) / ((A ⊃ B) . C) ⊃ (D . F) Exp.

e. (A Ú ~ B) . (C Ú ~ D) / ((A Ú ~ B) Ú C) . ((A Ú ~ B) Ú ~ D) Dist. 

 

a. ~ (A . B) Ú ~ (C . D) /\ ~ ((A . B) . (C . D)) DeM.

c. ~ (~ A ⊃ B) ⊃ (B Ú ~ A) /\ ~ (A Ú B) Ú (B Ú ~ A) C.E.

d. (A ⊃ B) ⊃ (C ⊃ (D . F)) /\ ((A ⊃ B) . C) ⊃ (D . F) Exp.

Step-by-step explanation

b. ~ ~ B ⊃ ~ ~ A /\ ~ ~ A ⊃ ~ ~ B Contrap. (not correct application because the negation symbol is not applied between the propositions after the contraposition)

e. (A Ú ~ B) . (C Ú ~ D) /\ ((A Ú ~ B) Ú C) . ((A Ú ~ B) Ú ~ D) Dist.  (not correct application, operators are interchanged (conjunction and disjunction symbols))