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Hard Time Understanding "If A C B, then A U B = B"
Understand how "If A [tex]\supseteq[/tex] B, then A U B = B" is possible.
None.
Since A U B = B, it can be separated into two cases. That is,
1) A U B [tex]\subseteq[/tex] B
2) B [tex]\subseteq[/tex] A U B
For case (1), I let x [tex]\in[/tex] A U B. Thus, either x [tex]\in[/tex] A or x [tex]\in[/tex] B. If x [tex]\in[/tex] A, then x [tex]\in[/tex] B. This means that A U B [tex]\subseteq[/tex] B.
For case (2), I let x [tex]\in[/tex] B. This is where I got stuck... I know I am supposed to apply the assumption that A [tex]\supseteq[/tex] B, but I am starting to think that it is impossible.
Here is an attachment of why I think it is impossible. Here is the link to tinypic for those who are too afraid to download attachments: http://tinypic.com/view.php?pic=xszle&s=7.
Can anyone give me a tip on how to approach this problem?
Homework Statement
Understand how "If A [tex]\supseteq[/tex] B, then A U B = B" is possible.
Homework Equations
None.
The Attempt at a Solution
Since A U B = B, it can be separated into two cases. That is,
1) A U B [tex]\subseteq[/tex] B
2) B [tex]\subseteq[/tex] A U B
For case (1), I let x [tex]\in[/tex] A U B. Thus, either x [tex]\in[/tex] A or x [tex]\in[/tex] B. If x [tex]\in[/tex] A, then x [tex]\in[/tex] B. This means that A U B [tex]\subseteq[/tex] B.
For case (2), I let x [tex]\in[/tex] B. This is where I got stuck... I know I am supposed to apply the assumption that A [tex]\supseteq[/tex] B, but I am starting to think that it is impossible.
Here is an attachment of why I think it is impossible. Here is the link to tinypic for those who are too afraid to download attachments: http://tinypic.com/view.php?pic=xszle&s=7.
Can anyone give me a tip on how to approach this problem?
Attachments

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