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Statement (A): Set S of real number is bounded above, if sup S is finite.
Statement (B): Set S of real numbers is unbounded above, if sup S = ∞
Statement (B): Set S of real numbers is unbounded above, if sup S = ∞
- a)A is true only
- b)B is false only
- c)A and B both true
- d)A and B both false
Correct answer is option 'C'. Can you explain this answer?
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Statement (A): Set S of real number is bounded above, if sup S is fini...
Infinity.
Statement (A) is true. If a set S of real numbers is bounded above, it means that there exists a real number M such that every element s in S satisfies s ≤ M. The supremum (sup) of S is defined as the least upper bound of S, meaning it is the smallest real number M' such that every element s in S satisfies s ≤ M'. If sup S is finite, it means that there exists a real number M' that is the supremum of S, and this M' serves as an upper bound for S.
Statement (B) is also true. If the supremum of a set S of real numbers is infinity, it means that there is no finite upper bound for S. In other words, S is unbounded above, as there is no real number M such that every element s in S satisfies s ≤ M.
Statement (A) is true. If a set S of real numbers is bounded above, it means that there exists a real number M such that every element s in S satisfies s ≤ M. The supremum (sup) of S is defined as the least upper bound of S, meaning it is the smallest real number M' such that every element s in S satisfies s ≤ M'. If sup S is finite, it means that there exists a real number M' that is the supremum of S, and this M' serves as an upper bound for S.
Statement (B) is also true. If the supremum of a set S of real numbers is infinity, it means that there is no finite upper bound for S. In other words, S is unbounded above, as there is no real number M such that every element s in S satisfies s ≤ M.
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Statement (A): Set S of real number is bounded above, if sup S is fini...
Sup S is a value that is the lowest upper bound of the set S. So if it is finite then it's bounded above otherwise that is not bounded above.
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Statement (A): Set S of real number is bounded above, if sup S is finite.Statement (B): Set S of real numbers is unbounded above, if sup S =∞a)A is true onlyb)B is false onlyc)A and B both trued)A and B both falseCorrect answer is option 'C'. Can you explain this answer?
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