Muft Shiksha
Update

Muft Shiksha™ एक 100% Free Education Portal है 🇮🇳, जिसका उद्देश्य Class 9–12 के हर विद्यार्थी तक High-Quality Education को पूरी तरह मुफ्त पहुँचाना है। 🇮🇳 हम मानते हैं कि अच्छी शिक्षा किसी student की आर्थिक स्थिति पर निर्भर नहीं होनी चाहिए। 🇮🇳 हर विद्यार्थी को वही Quality Study Material, MCQs, Quizzes, Exam Preparation, Concept-Based Learning और Bilingual Support मिलना चाहिए, जो आमतौर पर महंगी Coaching या Premium Platforms में मिलता है। Muft Shiksha™ 🇮🇳 इसी सोच के साथ बनाया गया है

Subjects

Mathematics

Introduction to Relations

संबंधों का परिचय

In Class 12 Mathematics, under the chapter Relations and Functions, Introduction to Relations explains a relation as a subset of a Cartesian product. Students learn to form and count relations on sets, and identify important examples such as empty, universal and identity relations. The topic also introduces conditions used to recognise reflexive and symmetric relations.

Practice questions

On (A={1,2,3,4}), if (aRb) when (a+b) is even, how many pairs are in (R)?On (A={1,2,3,4}), if (aRb) when (a+b) is odd, which statement about (R) is correct?On (A={1,2,3,4}), if (aRb) when (a) divides (b), which pair will not be in (R)?In the divisibility relation on ({1,2,3,6}), what are the least and greatest elements respectively?In the divisibility relation on ({2,3,6}), which is the least element?If divisibility relation is defined on (A={1,2,4,8}), what type of relation is it?If (R={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}) on (A={1,2,3}), what type of relation is (R)?If (R={(1,1),(2,2),(3,3),(1,2),(2,1)}) on (A={1,2,3}), why is (R) not a partial order relation?If (R) is a relation and (R^{-1}=R), which conclusion is definite?If (R={(1,2),(2,3),(3,1)}), which pair will be in (R^{-1}\circ R)?If (R={(1,2),(2,4),(3,4)}), which pair must be in (R^{-1})?If (R=A\times A) on (A={1,2,3}), which statement about (R) is false?If (A) is non-empty and (R=\varnothing), which statement is false?If (R={(1,1),(2,2),(3,3),(1,2),(1,3)}) on (A={1,2,3}), is (R) antisymmetric?If a relation is both symmetric and antisymmetric, what is correct for distinct elements (a\ne b)?If (R={(1,1),(2,2),(3,3),(1,2),(2,3)}) on (A={1,2,3}), why is (R) not a partial order relation?If (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,4),(1,4)}) on (A={1,2,3,4}), what is the correct statement about (R)?On (A={1,2,3}), relation (R) is defined by (aRb) if (|a-b|\le1). Which property is absent?On (A={1,2,3,4}), if (aRb) when (|a-b|) is divisible by (2), what type of relation is (R)?On (A={1,2,3,4}), if (aRb) when (a+b=5), which statement about (R) is correct?