diff --git a/chapter_6/exercises.md b/chapter_6/exercises.md index 45f20f2..cc254f0 100644 --- a/chapter_6/exercises.md +++ b/chapter_6/exercises.md @@ -2665,29 +2665,43 @@ Prove each statement in 39-44. a. $(A - B) \cup (B - A) \cup (A \cap B) = A \cup B$ +Omitted. + b. The sets $(A - B)$, $(B - A)$, and $(A \cap B)$ are mutually disjoint. +Omitted. + 40. For every positive integer $n$, if $A$ and $B_1, B_2, B_3, \dots$ are any sets, then $$ A \cap \left(\bigcup_{i = 1}^{n}B_i\right) = \bigcup_{i = 1}^{n}(A \cap B_i) $$ +Omitted. + 41. For every positive integer $n$, if $A_1, A_2, A_3, \dots$ and $B$ are any sets, then $$ \bigcap_{i = 1}^{n}(A_i - B) = \left(\bigcup_{i = 1}^{n}A_i\right) - B $$ +Omitted. + 42. For every positive integer $n$, if $A_1, A_2, A_3, \dots$ and $B$ are any sets, then $$ \bigcap_{i = 1}^{n}(A_i - B) = \left(\bigcap_{i = 1}^{n}A_i\right) - B $$ +Omitted. + 43. For every positive integer $n$, if $A$ and $B_1, B_2, B_3, \dots$ are any sets, then $$ \bigcup_{i = 1}^{n}(A \times B_i) = A \times \left(\bigcup_{i = 1}^{n}B_i\right) $$ +Omitted. + 44. For every positive integer $n$, if $A$ and $B_1, B_2, B_3, \dots$ are any sets, then $$ \bigcap_{i = 1}^{n}(A \times B_i) = A \times \left(\bigcap_{i = 1}^{n}B_i\right) $$ + +Omitted.