Question 1 |

Consider the following statements:

P: Good mobile phones are not cheap

Q: Cheap mobile phones are not good

L: P implies Q

M: Q implies P

N: P is equivalent to Q

Which one of the following about L, M, and N is CORRECT?

P: Good mobile phones are not cheap

Q: Cheap mobile phones are not good

L: P implies Q

M: Q implies P

N: P is equivalent to Q

Which one of the following about L, M, and N is CORRECT?

Only L is TRUE. | |

Only M is TRUE. | |

Only N is TRUE. | |

L, M and N are TRUE. |

Question 1 Explanation:

Question 2 |

Let x and Y be finite sets and f:x\rightarrowY be a function. Which one of the following statements is TRUE?

For any subsets A and B of x, |f(A\cupB)|=|f(A)|+|f(B)| | |

For any subsets A and B of x, f(A\capB) =f(A)\capf(B) | |

For any subsets A and B of x, |f(A\capB)| = min{|f (A)| ,|f(B)|} | |

For any subsets S and T of Y, f^{-1}(S\cap T)=f^{-1}(S)\cap f^{-1}(T) |

Question 2 Explanation:

Question 3 |

Let G be a group with 15 elements. Let L be a subgroup of G. It is known that L\neqG and that the size of L is at least 4. The size of L is _______.

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5 | |

6 | |

7 |

Question 3 Explanation:

Question 4 |

Which one of the following statements is TRUE about every n x n matrix with only real
eigenvalues?

If the trace of the matrix is positive and the determinant of the matrix is negative, at least one of its eigenvalues is negative. | |

If the trace of the matrix is positive, all its eigenvalues are positive. | |

If the determinant of the matrix is positive, all its eigenvalues are positive. | |

If the product of the trace and determinant of the matrix is positive, all its eigenvalues are positive. |

Question 4 Explanation:

Question 5 |

If V1 and V2 are 4-dimensional subspaces of a 6-dimensional vector space V, then the smallest possible dimension of V1\capV2 is _______.

1 | |

2 | |

3 | |

4 |

Question 5 Explanation:

There are 5 questions to complete.