Question 1 |

In a population of N families, 50% of the families have three children, 30% of the families have two children and the remaining families have one child. What is the probability that a randomly picked child belongs to a family with two children?

\left(\dfrac{3}{23}\right) | |

\left(\dfrac{6}{23}\right) | |

\left(\dfrac{3}{10}\right) | |

\left(\dfrac{3}{5}\right) |

Question 1 Explanation:

Question 2 |

In a class of 200 students, 125 students have taken Programming Language course, 85 students have taken Data Structures course, 65 students have taken Computer Organization course; 50 students have taken both Programming Language and Data Structures, 35 students have taken both Programming Language and Computer Organization; 30 students have taken both Data Structures and Computer Organization, 15 students have taken all the three courses.
How many students have not taken any of the three courses?

15 | |

20 | |

25 | |

30 |

Question 2 Explanation:

Question 3 |

Let a(x, y), b(x, y,) and c(x, y) be three statements with variables x and y chosen from some universe. Consider the following statement:

\qquad(\exists x)(\forall y)[(a(x, y) \wedge b(x, y)) \wedge \neg c(x, y)]

Which one of the following is its equivalent?

\qquad(\exists x)(\forall y)[(a(x, y) \wedge b(x, y)) \wedge \neg c(x, y)]

Which one of the following is its equivalent?

(\forall x)(\exists y)[(a(x, y) \vee b(x, y)) \to c(x, y)] | |

(\exists x)(\forall y)[(a(x, y) \vee b(x, y)) \wedge\neg c(x, y)] | |

\neg (\forall x)(\exists y)[(a(x, y) \wedge b(x, y)) \to c(x, y)] | |

\neg (\forall x)(\exists y)[(a(x, y) \vee b(x, y)) \to c(x, y)] |

Question 3 Explanation:

Question 4 |

Let R_{1} be a relation from A =\left \{ 1,3,5,7 \right \} to B = \left \{ 2,4,6,8 \right \}. R_{2} be another relation from B to C = {1, 2, 3, 4} as defined below:

i. An element x in A is related to an element y in B (under R_{1}) if x + y is divisible by 3.

ii. An element x in B is related to an element y in C (under R_{2}) if x + y is even but not divisible by 3.

Which is the composite relation R_{1}R_{2} from A to C?

i. An element x in A is related to an element y in B (under R_{1}) if x + y is divisible by 3.

ii. An element x in B is related to an element y in C (under R_{2}) if x + y is even but not divisible by 3.

Which is the composite relation R_{1}R_{2} from A to C?

R_{1}R_{2} = {(1, 2), (1, 4), (3, 3), (5, 4), (7, 3)} | |

R_{1}R_{2} = {(1, 2), (1, 3), (3, 2), (5, 2), (7, 3)} | |

R_{1}R_{2} = {(1, 2), (3, 2), (3, 4), (5, 4), (7, 2)} | |

R_{1}R_{2} = {(3, 2), (3, 4), (5, 1), (5, 3), (7, 1)} |

Question 4 Explanation:

Question 5 |

What is the maximum number of edges in an acyclic undirected graph with n vertices?

n-1 | |

n | |

n+1 | |

2n-1 |

Question 5 Explanation:

There are 5 questions to complete.