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Question Details

Board | CBSE |

Book | NCERT Textbook |

Class | 12 |

Subject | Mathematics |

Chapter | 1 [Relations and Functions] |

Exercise | 1.1 |

Question No. | 7 |

Question Type | Exercise |

**Solution: **

\(A=\) all books in library.

\(R=\{(x, y): x\) and \(y\) have same number of pages \(\}\)

(a) Reflexive : \(R=\{(a, a): a\) and \(a\) have same number of pages \(\}\). True so reflexive.

(b) Symmetric: If \(R=\left\{\left(a_1, a_2\right): a_1\right.\) and \(a_2\) have same no. of pages \(\}\)

Thus, \(R=\left\{\left(a_2, a_1\right): a_2\right.\) and \(a_1\) will definitely have same no. of pages \(\}\). So, symmetric.

(c) Transitive : If \(R=\left\{\left(a_1, a_2\right)\right\}\) and \(R=\left\{\left(a_2, a_3\right)\right\}\)

So, \(a_1, a_2\) and \(a_3\) all three books will have same no. of pages. Thus, \(R=\left\{\left(a_1, a_3\right)\right\}\) is true. So reflexive. Therefore, equivalence relation.

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