Mathematics Exam > Mathematics Questions > Which of the following is not correct?a)Every...
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Which of the following is not correct?
- a)Every open interval is an open set
- b)Every open interval is a nbd of each of its points
- c)Every point of an open interval is an interior point.
- d)The set
is open.
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Which of the following is not correct?a)Every open interval is an open...
Let (a, b) be an interval and x ε (a, b) which implies that a < x < b.
Let c, d be two numbers sueh that a < c < x and n < d < h
implies a < c < x < d < b
implies x ε (c, d) ⊂ (a, b)
Thus, the given interval (a, b) contains an open interval containing the point x and is therefore a nbd of x. Hence, the open interval is a nbd ol each o f its points and is therefore an open set. Hence, every point of an open interval is an interior point. Now ‘o’ is an interior point o f the set
which does not lie in this
set. Hence, the set
is not open.
Let c, d be two numbers sueh that a < c < x and n < d < h
implies a < c < x < d < b
implies x ε (c, d) ⊂ (a, b)
Thus, the given interval (a, b) contains an open interval containing the point x and is therefore a nbd of x. Hence, the open interval is a nbd ol each o f its points and is therefore an open set. Hence, every point of an open interval is an interior point. Now ‘o’ is an interior point o f the set
which does not lie in this
set. Hence, the set
is not open.
Most Upvoted Answer
Which of the following is not correct?a)Every open interval is an open...
Let (a, b) be an interval and x ε (a, b) which implies that a < x < b.
Let c, d be two numbers sueh that a < c < x and n < d < h
implies a < c < x < d < b
implies x ε (c, d) ⊂ (a, b)
Thus, the given interval (a, b) contains an open interval containing the point x and is therefore a nbd of x. Hence, the open interval is a nbd ol each o f its points and is therefore an open set. Hence, every point of an open interval is an interior point. Now ‘o’ is an interior point o f the set
which does not lie in this
set. Hence, the set
is not open.
Let c, d be two numbers sueh that a < c < x and n < d < h
implies a < c < x < d < b
implies x ε (c, d) ⊂ (a, b)
Thus, the given interval (a, b) contains an open interval containing the point x and is therefore a nbd of x. Hence, the open interval is a nbd ol each o f its points and is therefore an open set. Hence, every point of an open interval is an interior point. Now ‘o’ is an interior point o f the set
which does not lie in this
set. Hence, the set
is not open.
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Which of the following is not correct?a)Every open interval is an open setb)Every open interval is a nbd of each of its pointsc)Every point of an open interval is an interior point.d)The setis open.Correct answer is option 'D'. Can you explain this answer?
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Which of the following is not correct?a)Every open interval is an open setb)Every open interval is a nbd of each of its pointsc)Every point of an open interval is an interior point.d)The setis open.Correct answer is option 'D'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Which of the following is not correct?a)Every open interval is an open setb)Every open interval is a nbd of each of its pointsc)Every point of an open interval is an interior point.d)The setis open.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following is not correct?a)Every open interval is an open setb)Every open interval is a nbd of each of its pointsc)Every point of an open interval is an interior point.d)The setis open.Correct answer is option 'D'. Can you explain this answer?.
Which of the following is not correct?a)Every open interval is an open setb)Every open interval is a nbd of each of its pointsc)Every point of an open interval is an interior point.d)The setis open.Correct answer is option 'D'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Which of the following is not correct?a)Every open interval is an open setb)Every open interval is a nbd of each of its pointsc)Every point of an open interval is an interior point.d)The setis open.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following is not correct?a)Every open interval is an open setb)Every open interval is a nbd of each of its pointsc)Every point of an open interval is an interior point.d)The setis open.Correct answer is option 'D'. Can you explain this answer?.
Solutions for Which of the following is not correct?a)Every open interval is an open setb)Every open interval is a nbd of each of its pointsc)Every point of an open interval is an interior point.d)The setis open.Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mathematics.
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