Fsc Part 1 Mathematics (Complete Solution)

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Q3

For each of the following sets, determine whether or not the set forms a group with respect to the indicated operation.

Set |
Operation |

i) The set of rational numbers |
x |

ii) The set of rational numbers |
+ |

iii) The set of positive rational numbers |
x |

iv) The set of integers |
+ |

(v) The set of integers |
x |

Solution:

The set of rational number denoted by Q and the set of integers is denotad by Z.

Operation | ||

i) The set of rational numbers | x | Q is not a group under 'x' |

ii) The set of rational numbers | + | Q is a group under '+' |

iii) The set of positive rational numbers | x | This is a group |

iv) The set of integers | + | Z is a group under '+' |

(v) The set of integers | x | Z is not a group under 'x' |