Задача 69038 Упростить, используя основные тождества...

628a022a6653d96aeebf61ed

08.02.2023 17:16:43

Упростить, используя основные тождества алгебры множеств:

626fab9a354ab65fb2f43abb

08.02.2023 17:39:24

★

(A ∩ B ∩ C ∩ ~D) ∪ (~A ∩ C) ∪ (~B ∩ C) ∪ (C ∩ D) =

= [(A ∪ ~A) ∩ (B ∪ ~A) ∩ (C ∪ ~A) ∩ (~D ∪ ~A) ∩
∩ (A ∪ C) ∩ (B ∪ C) ∩ (C ∪ C) ∩ (~D ∪ C)] ∪
∪ [(~B ∪ C) ∩ (C ∪ C) ∩ (~B ∪ D) ∩ (C ∪ D)] =

= [1 ∩ (B ∪ ~A) ∩ (C ∪ ~A) ∩ (~D ∪ ~A) ∩
∩ (A ∪ C) ∩ (B ∪ C) ∩ C ∩ (~D ∪ C)] ∪
∪ [(~B ∪ C) ∩ C ∩ (~B ∪ D) ∩ (C ∪ D)] =

= [(B ∪ ~A) ∩ (~D ∪ ~A) ∩ C] ∪ [C ∩ (~B ∪ D)] =

= (C ∩ B ∩ ~D) ∪ (C ∩ ~A ∩ ~D) ∪ (C ∩ B ∩ ~A) ∪
∪ (C ∩ ~A ∩ ~A) ∪ (C ∩ ~B) ∪ (C ∩ D) =

= (C ∩ B ∩ ~D) ∪ (C ∩ ~A ∩ ~D) ∪ (C ∩ B ∩ ~A) ∪
∪ (C ∩ ~A) ∪ (C ∩ ~B) ∪ (C ∩ D) =

= (B ∩ C ∩ ~D) ∪ (~A ∩ C) ∪ (~B ∩ C) ∪ (C ∩ D)

Кажется, это всё, что можно сделать.