M1 Explore and Discuss 2

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.

1. Suppose A∩B≠∅, A∩C≠∅, and B∩C≠∅. Can you conclude that A∩B∩C≠∅? Explain your answer.
2. Suppose A∩B∩C≠∅. Can you conclude that A∩B≠∅, A∩C≠∅, and B∩C≠∅? Explain your answer.

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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