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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. | 4 |

Question Type | Exercise |

\(R=\{(a, b): a \leq b\}\)

(a) Reflexive : \(R=\{(a, a): a \leq a\}\) so reflexive.

(b) Symmetric : \(R=\left\{\left(a_1, a_2\right): a_1 \leq a_2\right\}\)

\(R=\left(a_2, a_1\right): a_2 \leq a_1\) so not symmetric.

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

\(R=\left\{\left(a_2, a_3\right): a_2 \leq a_3\right\}\)

Thus, \(a_1 \leq a_2 \leq a_3\)

\(\Rightarrow a_1 \leq a_3\) so transitive.

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