Question 1 |

The statement (\neg p)\Rightarrow (\neg q) is logically equivalent to which of the statements below?

I. p\Rightarrow q

II. q \Rightarrow p

III. (\neg q)\vee p

IV. (\neg p)\vee q

I. p\Rightarrow q

II. q \Rightarrow p

III. (\neg q)\vee p

IV. (\neg p)\vee q

I only | |

I and IV only | |

II only | |

II and III only |

Question 1 Explanation:

Question 2 |

Consider the first-order logic sentence F:\forall x(\exists yR(x,y)). Assuming non-empty logical
domains, which of the sentences below are implied by F?

I. \exists y(\exists xR(x,y))

II. \exists y(\forall xR(x,y))

III. \forall y(\exists xR(x,y))

IV. \neg \exists x(\forall y\neg R(x,y))

I. \exists y(\exists xR(x,y))

II. \exists y(\forall xR(x,y))

III. \forall y(\exists xR(x,y))

IV. \neg \exists x(\forall y\neg R(x,y))

IV only | |

I and IV only | |

II only | |

II and III only |

Question 2 Explanation:

Question 3 |

Let c_{1}....c_{n} be scalars, not all zero, such that \sum_{i=1}^{n}c_{i}a_{i}=0

where a_{i} are column vectors in R^{n}. Consider the set of linear equations Ax = b

where A=a_{1}....a_{n} and b=\sum_{i=1}^{n}a_{i}. The set of equations has

where a_{i} are column vectors in R^{n}. Consider the set of linear equations Ax = b

where A=a_{1}....a_{n} and b=\sum_{i=1}^{n}a_{i}. The set of equations has

a unique solution at x=J_{n} where J_{n} denotes a n-dimensional vector of all 1 | |

no solution | |

infinitely many solutions | |

finitely many solutions |

Question 3 Explanation:

Question 4 |

Consider the following functions from positive integers to real numbers:

10,\sqrt{n},n, log_{2}n,\frac{100}{n}.

The CORRECT arrangement of the above functions in increasing order of asymptotic complexity is:

10,\sqrt{n},n, log_{2}n,\frac{100}{n}.

The CORRECT arrangement of the above functions in increasing order of asymptotic complexity is:

log_{2}n,\frac{100}{n}, 10,\sqrt{n},n | |

\frac{100}{n}, 10,log_{2}n, \sqrt{n}, n | |

10, \frac{100}{n}, \sqrt{n}, log_{2}n, n | |

\frac{100}{n}, log_{2}n, 10, \sqrt{n}, n |

Question 4 Explanation:

Question 5 |

Consider the following table:

Match the algorithms to the design paradigms they are based on.

Match the algorithms to the design paradigms they are based on.

P-(ii), Q-(iii),R-(i) | |

P-(iii), Q-(i), R-(ii) | |

P-(ii), Q-(i), R-(iii) | |

P-(i), Q-(ii), R-(iii) |

Question 5 Explanation:

There are 5 questions to complete.