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Given a collection of points P in the plane, a 1-set is a point in P that can be separated from the rest by a line, that is the point lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P). The minimum value of n1(P) over all configurations P of 5 points in the plane in general position (that is no three points in P lie on a line) is
- a)3
- b)5
- c)2
- d)e) isa)3b)5c) 2
Correct answer is option 'B'. Can you explain this answer?
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Given a collection of points P in the plane, a 1-set is a point in P t...
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Introduction:
In this problem, we are given a collection of 5 points in the plane in general position. We need to determine the minimum number of 1-sets, where a 1-set is a point in the collection that can be separated from the rest by a line.
Approach:
To solve this problem, we will analyze the possible configurations of the 5 points and count the number of 1-sets in each configuration.
Configuration 1: All points are collinear
In this configuration, all 5 points lie on a single line. In this case, it is not possible to separate any point from the rest by a line. Therefore, the number of 1-sets is 0.
Configuration 2: 4 points are collinear
In this configuration, 4 points lie on a single line and the remaining point is not collinear with the other 4. In this case, the point that is not collinear can be separated from the rest by a line. Therefore, the number of 1-sets is 1.
Configuration 3: 3 points are collinear
In this configuration, 3 points lie on a single line and the remaining 2 points are not collinear with the other 3. In this case, we can separate each of the 2 non-collinear points from the rest by a line. Therefore, the number of 1-sets is 2.
Configuration 4: No points are collinear
In this configuration, no three points are collinear. In this case, we can draw a line through any pair of points, separating them from the remaining 3 points. Since there are 10 possible pairs of points (5 choose 2), we can separate the points into 10 different 1-sets. However, notice that each 1-set contains only 2 points, so we need to divide the total count by 2. Therefore, the number of 1-sets is 10/2 = 5.
Conclusion:
Out of all the possible configurations, the minimum number of 1-sets is 0 in configuration 1. Therefore, the correct answer is option B) 5.
In this problem, we are given a collection of 5 points in the plane in general position. We need to determine the minimum number of 1-sets, where a 1-set is a point in the collection that can be separated from the rest by a line.
Approach:
To solve this problem, we will analyze the possible configurations of the 5 points and count the number of 1-sets in each configuration.
Configuration 1: All points are collinear
In this configuration, all 5 points lie on a single line. In this case, it is not possible to separate any point from the rest by a line. Therefore, the number of 1-sets is 0.
Configuration 2: 4 points are collinear
In this configuration, 4 points lie on a single line and the remaining point is not collinear with the other 4. In this case, the point that is not collinear can be separated from the rest by a line. Therefore, the number of 1-sets is 1.
Configuration 3: 3 points are collinear
In this configuration, 3 points lie on a single line and the remaining 2 points are not collinear with the other 3. In this case, we can separate each of the 2 non-collinear points from the rest by a line. Therefore, the number of 1-sets is 2.
Configuration 4: No points are collinear
In this configuration, no three points are collinear. In this case, we can draw a line through any pair of points, separating them from the remaining 3 points. Since there are 10 possible pairs of points (5 choose 2), we can separate the points into 10 different 1-sets. However, notice that each 1-set contains only 2 points, so we need to divide the total count by 2. Therefore, the number of 1-sets is 10/2 = 5.
Conclusion:
Out of all the possible configurations, the minimum number of 1-sets is 0 in configuration 1. Therefore, the correct answer is option B) 5.
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Given a collection of points P in the plane, a 1-set is a point in P that can be separated from the rest by a line, that is the point lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P). The minimum value of n1(P) over all configurations P of 5 points in the plane in general position (that is no three points in P lie on a line) isa)3b)5c)2d)e) isa)3b)5c) 2Correct answer is option 'B'. Can you explain this answer?
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Given a collection of points P in the plane, a 1-set is a point in P that can be separated from the rest by a line, that is the point lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P). The minimum value of n1(P) over all configurations P of 5 points in the plane in general position (that is no three points in P lie on a line) isa)3b)5c)2d)e) isa)3b)5c) 2Correct answer is option 'B'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Given a collection of points P in the plane, a 1-set is a point in P that can be separated from the rest by a line, that is the point lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P). The minimum value of n1(P) over all configurations P of 5 points in the plane in general position (that is no three points in P lie on a line) isa)3b)5c)2d)e) isa)3b)5c) 2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given a collection of points P in the plane, a 1-set is a point in P that can be separated from the rest by a line, that is the point lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P). The minimum value of n1(P) over all configurations P of 5 points in the plane in general position (that is no three points in P lie on a line) isa)3b)5c)2d)e) isa)3b)5c) 2Correct answer is option 'B'. Can you explain this answer?.
Given a collection of points P in the plane, a 1-set is a point in P that can be separated from the rest by a line, that is the point lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P). The minimum value of n1(P) over all configurations P of 5 points in the plane in general position (that is no three points in P lie on a line) isa)3b)5c)2d)e) isa)3b)5c) 2Correct answer is option 'B'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Given a collection of points P in the plane, a 1-set is a point in P that can be separated from the rest by a line, that is the point lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P). The minimum value of n1(P) over all configurations P of 5 points in the plane in general position (that is no three points in P lie on a line) isa)3b)5c)2d)e) isa)3b)5c) 2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given a collection of points P in the plane, a 1-set is a point in P that can be separated from the rest by a line, that is the point lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P). The minimum value of n1(P) over all configurations P of 5 points in the plane in general position (that is no three points in P lie on a line) isa)3b)5c)2d)e) isa)3b)5c) 2Correct answer is option 'B'. Can you explain this answer?.
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