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Mathematics

Introduction to Relations

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.

Expert · Level 7 · 3 questions

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1. If \(S=\{1,2,3\}\) and \(A=\mathcal{P}(S)\), then a relation \(R\) on \(A\) is defined by \[R=\{(X,Y):X,Y\in A \text{ and } X\cup =S\}. \] How many diagonal pairs must be added to make \(R\) reflexive?

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2. On \(A=\mathcal{P}({1,2,3})\), \(R={(X,Y):X\setminus Y=X}\). How many diagonal pairs are in (R)?

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3. If \(A=\mathcal{P}({1,2,3})) and (R={(X,Y):X\triangle Y\subseteq X}\), what is (R) with respect to reflexivity?

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Reflexive
Not reflexive
Only for empty set
Universal

Introduction to Relations

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If \(S=\{1,2,3\}\) and \(A=\mathcal{P}(S)\), then a relation \(R\) on \(A\) is defined by \[R=\{(X,Y):X,Y\in A \text{ and } X\cup =S\}.
\] How many diagonal pairs must be added to make \(R\) reflexive?

On \(A=\mathcal{P}({1,2,3})\), \(R={(X,Y):X\setminus Y=X}\). How many diagonal pairs are in (R)?

If \(A=\mathcal{P}({1,2,3})) and (R={(X,Y):X\triangle Y\subseteq X}\), what is (R) with respect to reflexivity?

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Introduction to Relations

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On \(A=\mathcal{P}({1,2,3})\), \(R={(X,Y):X\setminus Y=X}\). How many diagonal pairs are in (R)?समुच्चय \(A=\mathcal{P}({1,2,3})\) पर \(R={(X,Y):X\setminus Y=X}\) है। (R) में कितने विकर्ण युग्म हैं?

If \(A=\mathcal{P}({1,2,3})) and (R={(X,Y):X\triangle Y\subseteq X}\), what is (R) with respect to reflexivity?यदि \(A=\mathcal{P}({1,2,3})) और (R={(X,Y):X\triangle Y\subseteq X}\) है, तो (R) कैसा है?

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On \(A=\mathcal{P}({1,2,3})\), \(R={(X,Y):X\setminus Y=X}\). How many diagonal pairs are in (R)?

If \(A=\mathcal{P}({1,2,3})) and (R={(X,Y):X\triangle Y\subseteq X}\), what is (R) with respect to reflexivity?