Suppose that A, B and C are subsets of X. Use examples of these sets to investing the following:
A Venn diagram is useful way of representing sets. If A is a subset of X, then
Solution
A U (B n C) = (A U B) n (A U C): Now we\'ll prove that A U (B n C)? (A U B) n
(A U C), and (A U B) n (A U C) ? A U (B n C) A U (B n C) = (A U B) n (A U C) follows.
======================================… A U (B n C)? (A U B) n (A U C),
Statament (1.1) proof: Let x? A U (B n C), then x?A or x? (B n C). a) Suppose first that x?A
then x? A U B and x? A U B, so: x?(A U B)n(A U C). b) suppose now that x? (B n C), then x?B
and x?C, hence x?(A U B) n (A U C). we obtain that A U (B n C)? (A U B) n (A U C)
======================================… (A U B) n (A U C) ? A U (B n C)
Statement (1.2) let x?(A U B) n (A U C) , then x?(A U B) and x?(A U C), if x?A it\'s simple to
show (1.2) is true. Suppose that x?B and x?C then x?(B n C) hence x?A U (B n C).
======================================… Statements (1.1) and (1.2) mean A U (B
n C) = (A U B) n (A U C):.
Suppose that A, B and C are subsets of X. Use examples of these sets .pdf
1. Suppose that A, B and C are subsets of X. Use examples of these sets to investing the following:
A Venn diagram is useful way of representing sets. If A is a subset of X, then
Solution
A U (B n C) = (A U B) n (A U C): Now we'll prove that A U (B n C)? (A U B) n
(A U C), and (A U B) n (A U C) ? A U (B n C) A U (B n C) = (A U B) n (A U C) follows.
======================================… A U (B n C)? (A U B) n (A U C),
Statament (1.1) proof: Let x? A U (B n C), then x?A or x? (B n C). a) Suppose first that x?A
then x? A U B and x? A U B, so: x?(A U B)n(A U C). b) suppose now that x? (B n C), then x?B
and x?C, hence x?(A U B) n (A U C). we obtain that A U (B n C)? (A U B) n (A U C)
======================================… (A U B) n (A U C) ? A U (B n C)
Statement (1.2) let x?(A U B) n (A U C) , then x?(A U B) and x?(A U C), if x?A it's simple to
show (1.2) is true. Suppose that x?B and x?C then x?(B n C) hence x?A U (B n C).
======================================… Statements (1.1) and (1.2) mean A U (B
n C) = (A U B) n (A U C):
