Show that if A and B are sets then (A intersection B) union (A intersection B compliment) = A first by showing that each side is a subset of the other side and then by using a membership table.

in Algebra 1 Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

  1. If element x belongs to set B and set A, the intersection A∩B also contains x. Not B (complement) does not contain x, so the intersection with A does not contain x.
  2. If x does not belong to set B but does belong to set A, A∩B does not contain x, but since not B does, its intersection with A contains x.
  3. If x does not belong to set A, then neither intersection contains x.
  4. If we consider the union of the two intersections from 1 and 2 above, x belongs to the union in each case.
  5. For 3 above, the union does not contain x.

For all elements x in A, the final union consists of all such elements, therefore the union is set A itself.

 

by Top Rated User (642k points)

Related questions

1 answer
1 answer
asked Aug 9, 2013 in Other Math Topics by Joystar1977 Level 1 User (220 points) | 139 views
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
82,894 questions
87,502 answers
1,964 comments
3,946 users