Relations and Functions
Madhya Pradesh Board · Class 12 · Mathematics
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Explore the full setClassify the relation R = {(a,b) : a - b = 10} on A = {1,2,3,4}.
Answer
Step 1: Check whether any pair from A satisfies a - b = 10. Step 2: The largest possible value of a - b in A is 4 - 1 = 3. Step 3: So no pair satisfies the condition. Answer: R is the empty relation.
संबंध R = {(a,b) : a - b = 10} on A = {1,2,3,4} को वर्गीकृत करें।
Answer
चरण 1: जांचें कि क्या A से कोई भी युग्म a - b = 10. को संतुष्ट करता है। चरण 2: A में a - b का सबसे बड़ा संभावित मान 4 - 1 = 3. है। चरण 3: इसलिए कोई भी युग्म शर्त को संतुष्ट नहीं करता है। उत्तर: R रिक्…
A = {1,2,3,4} पर संबंध R' = {(a,b) : |a-b| ≥ 0} को वर्गीकृत करें।
Answer
चरण 1: किसी भी वास्तविक संख्या a और b के लिए, |a-b| हमेशा गैर-नकारात्मक होता है। चरण 2: तो A × A में प्रत्येक जोड़ी इस शर्त को पूरा करती है। उत्तर: R' सार्वत्रिक संबंध है।…
Classify the relation R' = {(a,b) : |a-b| ≥ 0} on A = {1,2,3,4}.
Answer
Step 1: For any real numbers a and b, |a-b| is always non-negative. Step 2: So every pair in A × A satisfies the condition. Answer: R' is the universal relation.
Why are empty relation and universal relation called trivial relations?
Answer
Empty relation contains no ordered pair, while universal relation contains all ordered pairs in A × A. Because they are the two extreme cases of relations, they are called trivial relations. Quick che…
रिक्त संबंध और सार्वभौमिक संबंध को तुच्छ संबंध क्यों कहा जाता है?
Answer
रिक्त संबंध में कोई क्रमित युग्म नहीं होता है, जबकि सार्वत्रिक संबंध में A × A के सभी क्रमित युग्म होते हैं। क्योंकि वे संबंधों के दो चरम मामले हैं, इसलिए उन्हें तुच्छ संबंध कहा जाता है। त्वरित जांच: …
{1,2,3} पर R = {(1,1),(2,2),(3,3),(1,2),(2,3)} संबंध के लिए, रिफ्लेक्सिव, सिमेट्रिक और ट्रांजिटिव गुणों की जाँच करें।
Answer
चरण 1: परावर्ती? हाँ, क्योंकि (1,1), (2,2), और (3,3) मौजूद हैं। चरण 2: सममित? नहीं, क्योंकि (1,2), R में है लेकिन (2,1) नहीं है। चरण 3: संक्रामक? नहीं, क्योंकि (1,2) और (2,3), R में हैं, लेकिन (1,3) न…
For the relation R = {(1,1),(2,2),(3,3),(1,2),(2,3)} on {1,2,3}, check reflexive, symmetric, and transitive properties.
Answer
Step 1: Reflexive? Yes, because (1,1), (2,2), and (3,3) are present. Step 2: Symmetric? No, because (1,2) is in R but (2,1) is not. Step 3: Transitive? No, because (1,2) and (2,3) are in R, but (1,3) …
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