Suppose you have to use an element argument to prove the following statement. (Assume that all sets are subsets of a universal set U.) For all sets A, B, and C (A – B) n (C - B) C (AnC)- B. Consider the sentences in the following scrambled list. • Therefore a E (AnC)- B by the definition of set difference. • We must show that E (AnC)- B. • Thus x € An C by definition of intersection, and, in addition, a ¢ B. Thus, by definition of intersection, x € A and x E C, and, in addition, x B. By definition of intersection, те (А - В)П (С — B). • By definition of intersection, E A - B and x E C - B. Suppose A, B, and C are any sets and x E (AnC) - B. We must show that a E (A - B) n (C - B). Suppose A, B, and C are any sets and те (А - В)n(С - В). • By definition of set difference, r E A - B and x € C - B. • By definition of set difference, r E A and a ¢ B and a e C and a ¢ B. • By definition of intersection, r E A and a B and æ € C and e¢B.
Suppose you have to use an element argument to prove the following statement. (Assume that all sets are subsets of a universal set U.) For all sets A, B, and C (A – B) n (C - B) C (AnC)- B. Consider the sentences in the following scrambled list. • Therefore a E (AnC)- B by the definition of set difference. • We must show that E (AnC)- B. • Thus x € An C by definition of intersection, and, in addition, a ¢ B. Thus, by definition of intersection, x € A and x E C, and, in addition, x B. By definition of intersection, те (А - В)П (С — B). • By definition of intersection, E A - B and x E C - B. Suppose A, B, and C are any sets and x E (AnC) - B. We must show that a E (A - B) n (C - B). Suppose A, B, and C are any sets and те (А - В)n(С - В). • By definition of set difference, r E A - B and x € C - B. • By definition of set difference, r E A and a ¢ B and a e C and a ¢ B. • By definition of intersection, r E A and a B and æ € C and e¢B.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.4: Binary Operations
Problem 14E: Assume that is a binary operation on a non empty set A, and suppose that is both commutative and...
Related questions
Topic Video
Question
Transcribed Image Text:Suppose you have to use an element argument to
prove the following statement. (Assume that all sets
are subsets of a universal set U.)
For all sets A, B, and C
(A – B) n (C - B) C (AnC)- B.
Consider the sentences in the following scrambled list.
• Therefore a E (AnC) - B by the definition of
set difference.
• We must show that E (AnC)- B.
• Thus x € AnC by definition of intersection,
and, in addition, x ¢ B.
• Thus, by definition of intersection, x € A and
x€ C, and, in addition, a4 B.
• By definition of intersection,
те (А — В)П (С — B).
• By definition of intersection, r E A - B and
TE C - B.
Suppose A, B, and C are any sets and
x E (AnC) – B.
• We must show that a E (A B) n(C- B).
• Suppose A, B, and C are any sets and
хе (А- В)n(С - В).
• By definition of set difference, E A-B and
x € C - B.
• By definition of set difference, r E A and a B
and a € C and a ¢ B.
• By definition of intersection, a € A and a B
and æ e C and e ¢ B.
Expert Solution
Step 1
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,