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An (B-A) = 0

An (B-A) = 0

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 14CT
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Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Click and drag the given steps to their corresponding step number to prove the given statement. (A-B) CCA- C. Reset Step 1 Step 2 Step 3 Step 4 Then x is in A - B and in C. Suppose that x E (A - B) - C x EA and x E C. This shows that x EA - C. Since x EA-B, XEA. XEA and x E C. This shows that Xx EA - C. Then x is in A - B but not in C.
Transcribed Image Text:Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Click and drag the given steps to their corresponding step number to prove the given statement. (A-B) CCA- C. Reset Step 1 Step 2 Step 3 Step 4 Then x is in A - B and in C. Suppose that x E (A - B) - C x EA and x E C. This shows that x EA - C. Since x EA-B, XEA. XEA and x E C. This shows that Xx EA - C. Then x is in A - B but not in C.
Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Click and drag the steps on the left to their corresponding step number on the right to prove the given statement. An (B-A) = 0 By definition of set difference, x belonging to B-A means that x is in B and x is not in A. Therefore, An (B-A) is empty. Suppose that An (B-A) is non empty set and x belongs to An (B-A). Then x belong to A and x belong to B - A. Therefore, x is in A and x is not in A. That is a contradiction. By definition of set difference, x belonging to B-A means that x is in B and x is in A. Therefore, An (B-A) is not empty. Therefore, x is in A and x is in A.
Transcribed Image Text:Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Click and drag the steps on the left to their corresponding step number on the right to prove the given statement. An (B-A) = 0 By definition of set difference, x belonging to B-A means that x is in B and x is not in A. Therefore, An (B-A) is empty. Suppose that An (B-A) is non empty set and x belongs to An (B-A). Then x belong to A and x belong to B - A. Therefore, x is in A and x is not in A. That is a contradiction. By definition of set difference, x belonging to B-A means that x is in B and x is in A. Therefore, An (B-A) is not empty. Therefore, x is in A and x is in A.
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