Question

Дано: A = [ 1; 5), B = (2; +∞), с= (-∞; 3). Найти: 1) (A ∪ B) ∩ (A ∪ C) ; 2) (A ∩ B) ∪ (B ∩ C) Дам 70 баллов

Answer 1

$A=[\ 1;5)\ \ ,\ \ B=(2;+\infty )\ \ ,\ \ C=(-\infty ;3)\\\\1)\ \ A\cup B=[\, 1;+\infty )\ \ ,\ \ \ A\cup C=(-\infty ;5)\\\\(A\cup B)\cap (A\cup C)=[\ 1\, ;5\, )\\\\2)\ \ A\cap B=(\, 2\, ;\, 5\, )\ \ ,\ \ \ B\cap C=(\, 2\, ;\, 3\, )\\\\(A\cap B)\cup (B\cap C)=(\, 2;\, 5\, )$