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Homework answers / question archive / M1 Explore and Discuss 2 Original Post: Complete the following "Explore and Discuss" tasks from 6
Original Post: Complete the following "Explore and Discuss" tasks from 6.1, page 351 in the text.
Let A,B, and C be nonempty subsets of a set U.
NOTE 1: If you think the answer is yes, you need to explain why it is true no matter what the sets are. If you think it is false, you only need to provide one counter-example.
NOTE 2: Pay careful attention to the notation. You are being told that the various intersections are not empty.
Response Posts: Respond to the posts of at least 2 other students. You may ask a question or offer feedback. NOTE: Your grade on this assignment is based on both your original and response posts.
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M1 Explore and Discuss 2
Let A be the set with elements {1,2,3,4,5}, B be the set with elements {1,5,6,7} and C be the set with elements {3,6,7,8,9}. The intersection A∩B has the elements {1,5} while A∩C has the element {3} and B∩C has the elements {6,7}. However, the intersection A∩B∩C does not have an element, therefore, we cannot conclude that A∩B∩C≠∅.
For the second question, the answer is yes, since the intersection of three sets is not empty, then any two of those sets will have an intersection with elements including the elements of the intersection of all the three sets. If any two of these sets don’t have an intersection, then the intersection of all three sets is a null set.
