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sav07_homework_1_solution [2007/03/19 12:00] wikiadmin |
sav07_homework_1_solution [2007/03/19 12:02] wikiadmin |
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holds. Namely, suppose <latex>(x,z) \in r \circ (s \cap t)</latex>. | holds. Namely, suppose <latex>(x,z) \in r \circ (s \cap t)</latex>. | ||
Then there is a y such | Then there is a y such | ||
- | that <latex>(x,y) \in r</latex> and <latex>(y,z) \in s \cap t</latex>. Therefore, | + | that <latex>(x,y) \in r</latex> and <latex>(y,z) \in s \cap t </latex>. Therefore, |
<latex>(y,z) \in s</latex> and <latex>(y,z) \in t</latex>. From <latex>(x,y) \in r</latex> and <latex>(y,z) \in s</latex> we | <latex>(y,z) \in s</latex> and <latex>(y,z) \in t</latex>. From <latex>(x,y) \in r</latex> and <latex>(y,z) \in s</latex> we | ||
have <latex>(x,z) \in r \circ s</latex>. Similarly, | have <latex>(x,z) \in r \circ s</latex>. Similarly, |