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(Solved) 3) Let S, T be non-empty bounded sets of real numbers. Which one of the following statement is implied by supS < sup T 7 (1) There exists an


these 3 questions are about math analysis.

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math131A-hw2-1.pngmath131A-hw2-2.png

3) Let S, T be non-empty bounded sets of real numbers. Which one of
the following statement is implied by supS < sup T 7 (1) There exists an upper bound of S belonging to T.
(2) There exists a lower bound of T belonging to S. Justify the answer! 4) Let 81 and 82 be two statements. Which of the following strategies is
not a valid way to show that ” 81 implies 82 ? (a) Assume that 81 is true and then use this to show that 82 is true. (b) Show that 81 implies some intermediate statement 8’ and then
show that 8’ implies 82. c) Assuming that 81 is true and 52 is false, deduce a contradiction.
d) Assune that 52 is false and then use this to show that 81 is false.
e) Assuming that 81 is false and 82 is true, deduce a contradiction.
f) At least one of 81 and 82 is true. (
(
(
(

 


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