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

Practice questions

01If \(S=\{1,2,3\}\) 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?

0 reads0 helpful★ – (0)

Answer and explanation

Correct answer: B. 7

Step 1: \(\mathcal{P}(S)\) has (8) elements, so (8) diagonal pairs are needed. Step 2: On the diagonal, (X\cup X=X), which equals (S) only when (X=S). Step 3: One diagonal pair is already present, so (7) must be added.

Question & solution Rate / view replies Report an issue

सुधार सुझाएँ / Earn

02On \(A=\mathcal{P}({1,2,3})\), \(R={(X,Y):X\setminus Y=X}\). How many diagonal pairs are in (R)?

0 reads0 helpful★ – (0)

Answer and explanation

Correct answer: A. 1

Step 1: On the diagonal, \(X\setminus X=\varnothing\). Step 2: The condition \(X\setminus X=X\) holds only when \(X=\varnothing\). Step 3: Hence only \((\varnothing,\varnothing)\) is a diagonal pair.

Question & solution Rate / view replies Report an issue

सुधार सुझाएँ / Earn

03If \(A=\mathcal{P}({1,2,3})) and (R={(X,Y):X\triangle Y\subseteq X}\), what is (R) with respect to reflexivity?

0 reads0 helpful★ – (0)

Answer and explanation

Correct answer: A. Reflexive

Step 1: On the diagonal, (X\triangle X=\varnothing). Step 2: The empty set is a subset of every set, so (\varnothing\subseteq X) is true. Step 3: Therefore all diagonal pairs are in the relation.

Question & solution Rate / view replies Report an issue

सुधार सुझाएँ / Earn

Introduction to Relations

Practice questions

02On \(A=\mathcal{P}({1,2,3})\), \(R={(X,Y):X\setminus Y=X}\). 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?

03If \(A=\mathcal{P}({1,2,3})) and (R={(X,Y):X\triangle Y\subseteq X}\), 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?

Analytics choices

02On \(A=\mathcal{P}({1,2,3})\), \(R={(X,Y):X\setminus Y=X}\). How many diagonal pairs are in (R)?

03If \(A=\mathcal{P}({1,2,3})) and (R={(X,Y):X\triangle Y\subseteq X}\), what is (R) with respect to reflexivity?