Question 1 |

In a certain town, the probability that it will rain in the afternoon is known to be 0.6. Moreover, meteorological data indicates that if the temperature at noon is less than or equal to 25^{\circ}C, the probability that it will rain in the afternoon is 0.4. The temperature at noon is equally likely to be above 25^{\circ}C, or at/below 25^{\circ}C. What is the probability that it will rain in the afternoon on a day when the temperature at noon is above 25^{\circ}C?

0.4 | |

0.6 | |

0.8 | |

0.9 |

Question 1 Explanation:

Question 2 |

For the set N of natural numbers and a binary operation f : N \times N \to N, an element z \in N is called an identity for f, if f (a, z) = a = f(z, a), for all a \in N. Which of the following binary operations have an identity?

i. f (x, y) = x + y - 3

ii. f (x, y) = \max(x, y)

iii. f (x, y) = x^y

i. f (x, y) = x + y - 3

ii. f (x, y) = \max(x, y)

iii. f (x, y) = x^y

I and II only | |

II and III only | |

I and III only | |

None of these |

Question 2 Explanation:

Question 3 |

In the automaton below, s is the start state and t is the only final state.

Consider the strings u = abbaba, v = bab, \text{ and } w = aabb. Which of the following statements is true?

Consider the strings u = abbaba, v = bab, \text{ and } w = aabb. Which of the following statements is true?

The automaton accepts u and v but not w | |

The automaton accepts each of u, v, and w | |

The automaton rejects each of u, v, and w | |

The automaton accepts u but rejects v and w |

Question 3 Explanation:

Question 4 |

In the context-free grammar below, S is the start symbol, a and b are terminals, and\epsilon denotes the empty string

S \rightarrow aSa \mid bSb \mid a \mid b \mid \epsilon

Which of the following strings is NOT generated by the grammar?

S \rightarrow aSa \mid bSb \mid a \mid b \mid \epsilon

Which of the following strings is NOT generated by the grammar?

aaaa | |

baba | |

abba | |

babaaabab |

Question 4 Explanation:

Question 5 |

Which regular expression best describes the language accepted by the non-deterministic automaton below?

(a + b)^* \ a(a + b)b | |

(abb)^* | |

(a + b)^* \ a(a + b)^* \ b(a + b)^* | |

(a + b)^* |

Question 5 Explanation:

There are 5 questions to complete.