संबंध \(R=\{(1,2),(2,3),(3,4)\}\) का प्रांत क्या है?
What is the domain of the relation \(R=\{(1,2),(2,3),(3,4)\}\)?
#domain
#relations
#ordered pairs
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A ({1,2,3})
B ({2,3,4})
C ({1,2,3,4})
D ({(1,2),(2,3),(3,4)})
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Correct Answer
A. ({1,2,3})
Step 1
Concept
The domain is the set of first components of ordered pairs. Here the first components are (1,2,3).
Step 2
Why this answer is correct
The correct answer is A. ({1,2,3}). The domain is the set of first components of ordered pairs. Here the first components are (1,2,3).
Step 3
Exam Tip
प्रांत क्रमित युग्मों के पहले अवयवों का समुच्चय होता है। यहां पहले अवयव (1,2,3) हैं।
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संबंध \(R=\{(2,5),(3,5),(4,6)\}\) का परिसर क्या है?
What is the range of the relation \(R=\{(2,5),(3,5),(4,6)\}\)?
#range
#relations
#basic
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A ({2,3,4})
B ({5,6})
C ({2,3,4,5,6})
D ({(2,5),(3,5)})
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Correct Answer
B. ({5,6})
Step 1
Concept
The range is the set of second components, and repeated values are written once. So the range is ({5,6}).
Step 2
Why this answer is correct
The correct answer is B. ({5,6}). The range is the set of second components, and repeated values are written once. So the range is ({5,6}).
Step 3
Exam Tip
परिसर क्रमित युग्मों के दूसरे अवयवों का समुच्चय होता है और दोहराव केवल एक बार लिखा जाता है। इसलिए परिसर ({5,6}) है।
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यदि \(A=\{1,2,3\}\), \(B=\{4,5\}\) और \(R=\{(1,4),(3,5)\}\) है, तो (R) का सहप्रांत क्या है?
If \(A=\{1,2,3\}\), \(B=\{4,5\}\), and \(R=\{(1,4),(3,5)\}\), what is the codomain of (R)?
#codomain
#range
#relations
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A ({1,3})
B ({4,5})
C ({1,2,3})
D ({(1,4),(3,5)})
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Correct Answer
B. ({4,5})
Step 1
Concept
For a relation from (A) to (B), the codomain is the whole set (B). The range may be a subset of the codomain.
Step 2
Why this answer is correct
The correct answer is B. ({4,5}). For a relation from (A) to (B), the codomain is the whole set (B). The range may be a subset of the codomain.
Step 3
Exam Tip
(A) से (B) में संबंध का सहप्रांत पूरा समुच्चय (B) होता है। परिसर सहप्रांत का उपसमुच्चय हो सकता है।
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यदि किसी संबंध का प्रांत ({1,2}) और परिसर ({5}) है, तो कौन-सा संबंध सही हो सकता है?
If a relation has domain ({1,2}) and range ({5}), which relation can be correct?
#domain
#range
#relations
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A ({(1,5),(2,5)})
B ({(1,5),(2,6)})
C ({(1,6),(2,6)})
D ({(5,1),(5,2)})
Explanation opens after your attempt
Correct Answer
A. ({(1,5),(2,5)})
Step 1
Concept
The first components give domain ({1,2}), and the second components give range ({5}). Therefore the first option is correct.
Step 2
Why this answer is correct
The correct answer is A. ({(1,5),(2,5)}). The first components give domain ({1,2}), and the second components give range ({5}). Therefore the first option is correct.
Step 3
Exam Tip
पहले अवयवों से प्रांत ({1,2}) और दूसरे अवयवों से परिसर ({5}) मिलता है। इसलिए पहला विकल्प सही है।
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यदि \(R=\{(1,3),(2,4)\}\) \(A=\{1,2\}\) से \(B=\{3,4,5\}\) में है, तो (R) का परिसर क्या है?
If \(R=\{(1,3),(2,4)\}\) is a relation from \(A=\{1,2\}\) to \(B=\{3,4,5\}\), what is the range of (R)?
#range
#codomain
#relations
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A ({1,2})
B ({3,4})
C ({3,4,5})
D ({1,2,3,4})
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Correct Answer
B. ({3,4})
Step 1
Concept
The range is formed only from second components actually appearing in the relation. (5) is in the codomain, but not in the range.
Step 2
Why this answer is correct
The correct answer is B. ({3,4}). The range is formed only from second components actually appearing in the relation. (5) is in the codomain, but not in the range.
Step 3
Exam Tip
परिसर केवल उन दूसरे अवयवों से बनता है जो संबंध में सच में आए हैं। (5) सहप्रांत में है, पर परिसर में नहीं है।
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यदि \(A=\{1,2,3\}\) पर संबंध \(R=\{(1,1),(2,2),(3,3)\}\) है, तो (R) का प्रांत क्या है?
If \(R=\{(1,1),(2,2),(3,3)\}\) is a relation on \(A=\{1,2,3\}\), what is the domain of (R)?
#domain
#identity relation
#relations
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A ({1})
B ({1,2,3})
C ({(1,1),(2,2),(3,3)})
D \(\varnothing\)
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Correct Answer
B. ({1,2,3})
Step 1
Concept
The domain is formed by the first components (1,2,3). The identity relation has the whole set (A) as its domain.
Step 2
Why this answer is correct
The correct answer is B. ({1,2,3}). The domain is formed by the first components (1,2,3). The identity relation has the whole set (A) as its domain.
Step 3
Exam Tip
प्रांत पहले अवयवों (1,2,3) से बनता है। तत्समक संबंध का प्रांत पूरा (A) होता है।
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यदि \(R=\varnothing\) है, तो उसका प्रांत क्या होगा?
If \(R=\varnothing\), what will be its domain?
#empty relation
#domain
#relations
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A \(\varnothing\)
B ({0})
C ({1})
D निर्धारित नहीं / Not defined
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Correct Answer
A. \(\varnothing\)
Step 1
Concept
The empty relation has no ordered pair, so it has no first component. Hence the domain is \(\varnothing\).
Step 2
Why this answer is correct
The correct answer is A. \(\varnothing\). The empty relation has no ordered pair, so it has no first component. Hence the domain is \(\varnothing\).
Step 3
Exam Tip
खाली संबंध में कोई क्रमित युग्म नहीं है, इसलिए कोई पहला अवयव भी नहीं है। अतः प्रांत \(\varnothing\) है।
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यदि \(R=\{(1,2),(2,3),(3,1)\}\) है, तो (R) का प्रांत और परिसर क्रमशः क्या हैं?
If \(R=\{(1,2),(2,3),(3,1)\}\), what are the domain and range respectively?
#domain
#range
#relations
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A ({1,2,3},{1,2,3})
B ({1,2},{2,3})
C ({2,3,1},{1})
D ({(1,2),(2,3)},{3,1})
Explanation opens after your attempt
Correct Answer
A. ({1,2,3},{1,2,3})
Step 1
Concept
The first components are (1,2,3), and the second components are (2,3,1), which as a set is ({1,2,3}). Be careful with set order.
Step 2
Why this answer is correct
The correct answer is A. ({1,2,3},{1,2,3}). The first components are (1,2,3), and the second components are (2,3,1), which as a set is ({1,2,3}). Be careful with set order.
Step 3
Exam Tip
पहले अवयव (1,2,3) हैं और दूसरे अवयव (2,3,1) हैं, जो समुच्चय के रूप में ({1,2,3}) है। क्रम लिखने में ध्यान रखें।
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यदि \(R=\{(1,1),(1,2),(2,2)\}\) है, तो (R) का परिसर क्या है?
If \(R=\{(1,1),(1,2),(2,2)\}\), what is the range of (R)?
#range
#relations
#duplicate values
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A ({1})
B ({2})
C ({1,2})
D ({(1,1),(2,2)})
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Correct Answer
C. ({1,2})
Step 1
Concept
The second components are (1,2,2), and after removing repetition we get ({1,2}). The range uses only second components.
Step 2
Why this answer is correct
The correct answer is C. ({1,2}). The second components are (1,2,2), and after removing repetition we get ({1,2}). The range uses only second components.
Step 3
Exam Tip
दूसरे अवयव (1,2,2) हैं और दोहराव हटाने पर ({1,2}) मिलता है। परिसर में केवल दूसरे अवयव लिए जाते हैं।
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यदि \(R=\{(1,a),(2,b),(3,c)\}\) है, तो (R) के प्रतिलोम का प्रांत क्या होगा?
If \(R=\{(1,a),(2,b),(3,c)\}\), what will be the domain of \(R^{-1}\)?
#inverse relation
#domain
#range
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A ({1,2,3})
B ({a,b,c})
C ({(a,1),(b,2),(c,3)})
D \(\varnothing\)
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Correct Answer
B. ({a,b,c})
Step 1
Concept
In the inverse relation, second components become first components. Hence the domain of \(R^{-1}\) is the range of (R), which is ({a,b,c}).
Step 2
Why this answer is correct
The correct answer is B. ({a,b,c}). In the inverse relation, second components become first components. Hence the domain of \(R^{-1}\) is the range of (R), which is ({a,b,c}).
Step 3
Exam Tip
प्रतिलोम में दूसरे अवयव पहले बन जाते हैं। इसलिए \(R^{-1}\) का प्रांत (R) के परिसर ({a,b,c}) के बराबर है।
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यदि \(R=\{(1,5),(2,6),(4,8)\}\) है, तो कौन-सा अवयव (R) के प्रांत में नहीं है?
If \(R=\{(1,5),(2,6),(4,8)\}\), which element is not in the domain of (R)?
#domain
#relations
#ordered pairs
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A (1)
B (2)
C (3)
D (4)
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Step 1
Concept
The domain is ({1,2,4}), so (3) is not in it. For domain, look only at the first components.
Step 2
Why this answer is correct
The correct answer is C. (3). The domain is ({1,2,4}), so (3) is not in it. For domain, look only at the first components.
Step 3
Exam Tip
प्रांत ({1,2,4}) है, इसलिए (3) इसमें नहीं है। प्रांत में केवल पहले अवयव देखे जाते हैं।
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यदि \(R=\{(1,2),(2,2),(3,2)\}\) है, तो कौन-सा कथन सही है?
If \(R=\{(1,2),(2,2),(3,2)\}\), which statement is correct?
#range
#domain
#relations
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A प्रांत ({2}) है / The domain is ({2})
B परिसर ({2}) है / The range is ({2})
C सहप्रांत ({1,2,3}) है / The codomain is ({1,2,3})
D प्रांत \(\varnothing\) है / The domain is \(\varnothing\)
Explanation opens after your attempt
Correct Answer
B. परिसर ({2}) है / The range is ({2})
Step 1
Concept
All second components are (2), so the range is ({2}). The domain would be ({1,2,3}).
Step 2
Why this answer is correct
The correct answer is B. परिसर ({2}) है / The range is ({2}). All second components are (2), so the range is ({2}). The domain would be ({1,2,3}).
Step 3
Exam Tip
दूसरे अवयव सभी (2) हैं, इसलिए परिसर ({2}) है। प्रांत ({1,2,3}) होगा।
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यदि \(A=\{1,2,3,4,5\}\) और \(R=\{(x,y):y=2x\}\), जहां \(x,y\in A\), तो (R) का परिसर क्या है?
If \(A=\{1,2,3,4,5\}\) and \(R=\{(x,y):y=2x\}\), where \(x,y\in A\), what is the range of (R)?
#range
#rule based relation
#relations
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A ({2,4})
B ({1,2})
C ({2,4,6,8,10})
D ({1,2,3,4,5})
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Correct Answer
A. ({2,4})
Step 1
Concept
For (x=1), (y=2), and for (x=2), (y=4); after that \(y\notin A\). So the range is ({2,4}).
Step 2
Why this answer is correct
The correct answer is A. ({2,4}). For (x=1), (y=2), and for (x=2), (y=4); after that \(y\notin A\). So the range is ({2,4}).
Step 3
Exam Tip
(x=1) पर (y=2) और (x=2) पर (y=4) मिलता है; आगे \(y\notin A\) हो जाता है। इसलिए परिसर ({2,4}) है।
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यदि \(A=\{1,2,3\}\) और \(R=\{(1,2),(2,3)\}\) है, तो कौन-सा अवयव (R) के प्रांत में है लेकिन परिसर में नहीं है?
If \(A=\{1,2,3\}\) and \(R=\{(1,2),(2,3)\}\), which element is in the domain of (R) but not in the range?
#domain
#range
#set difference
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A (1)
B (2)
C (3)
D \(\varnothing\)
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Step 1
Concept
The domain is ({1,2}), and the range is ({2,3}). Only (1) is in the domain but not in the range.
Step 2
Why this answer is correct
The correct answer is A. (1). The domain is ({1,2}), and the range is ({2,3}). Only (1) is in the domain but not in the range.
Step 3
Exam Tip
प्रांत ({1,2}) और परिसर ({2,3}) है। इनमें केवल (1) प्रांत में है लेकिन परिसर में नहीं है।
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