Question 1 |

Which one of the following in NOT necessarily a property of a Group?

Commutativity | |

Associativity | |

Existence of inverse for every element | |

Existence of identity |

Question 1 Explanation:

Question 2 |

What is the chromatic number of an n-vertex simple connected graph which does
not contain any odd length cycle? Assume n\geq2.

2 | |

3 | |

n-1 | |

n |

Question 2 Explanation:

Question 3 |

Which one of the following is TRUE for any simple connected undirected graph
with more than 2 vertices?

No two vertices have the same degree. | |

At least two vertices have the same degree. | |

At least three vertices have the same degree. | |

All vertices have the same degree. |

Question 3 Explanation:

Question 4 |

Consider the binary relation R = {(x,y), (x,z), (z,x), (z,y)} on the set {x,y,z}.
Which one of the following is TRUE?

R is symmetric but NOT antisymmetric | |

R is NOT symmetric but antisymmetric | |

R is both symmetric and antisymmetric | |

R is neither symmetric nor antisymmetric |

Question 4 Explanation:

Question 5 |

(1217)_{8} is equivalent to

(1217)_{16} | |

(028F)_{16} | |

(2297)_{10} | |

(0B17)_{16} |

Question 5 Explanation:

There are 5 questions to complete.