6 .
If R = {(1, 2),(2, 3),(3, 3)} be a relation defined on A= {1, 2, 3} then R . R (= R2) is

A. | {(1, 2),(1, 3),(3, 3)} |

B. | {(1, 3),(2, 3),(3, 3)} |

C. | {(2, 1),(1, 3),(2, 3)} |

D. | R itself |

7 .
Which of the following statements is false ?

A. | If R is relexive, then R ∩ R-1 ≠ φ |

B. | R ∩ R-1 ≠ φ =>R is anti-symmetric. |

C. | If R, R' are relexive relations in A, then R - R' is reflexive |

D. | If R, R' are equivalence relations in a set A, then R ∩ R' is also an equivalence relation in A |

8 .
If (G, .) is a group, such that (ab)2 = a2 b2 ∀ a, b ∈ G, then G is a/an

A. | abelian group |

B. | non-abelian group |

C. | commutative semi group |

D. | none of these |

10 .
Let G denoted the set of all n x n non-singular matrices with rational numbers as entries. Then under multiplication G is a/an

A. | subgroup |

B. | ininite, abelian |

C. | finite abelian group |

D. | infinite, non abelian group |

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