Question 1 |

Consider the following statements:

S1: The sum of two singular nxn matrices may be non-singular

S2: The sum of two nxn non-singular matrices may be singular.

Which of the following statements is correct?

S1: The sum of two singular nxn matrices may be non-singular

S2: The sum of two nxn non-singular matrices may be singular.

Which of the following statements is correct?

S1 and S2 are both true | |

S1 is true, S2 is false | |

S1 is false, S2 is true | |

S1 and S2 are both false |

Question 1 Explanation:

Question 2 |

Consider the following relations:

```
R1(a,b) iff (a+b) is even over the set of integers
R2(a,b) iff (a+b) is odd over the set of integers
R3(a,b) iff a.b > 0 over the set of non-zero rational numbers
R4(a,b) iff |a - b| <= 2 over the set of natural numbers
```

Which of the following statements is correct?R1 and R2 are equivalence relations, R3 and R4 are not | |

R1 and R3 are equivalence relations, R2 and R4 are not | |

R1 and R4 are equivalence relations, R2 and R3 are not | |

R1, R2, R3 and R4 are all equivalence relations |

Question 2 Explanation:

Question 3 |

Consider two well-formed formulas in prepositional logic.

F1: \; P\Rightarrow \neg P

F2: \;( P\Rightarrow \neg P)\vee ( \neg P\Rightarrow P)

Which of the following statements is correct?

F1: \; P\Rightarrow \neg P

F2: \;( P\Rightarrow \neg P)\vee ( \neg P\Rightarrow P)

Which of the following statements is correct?

F1 is satisfiable, F2 is valid | |

F1 unsatisfiable, F2 is satisfiable | |

F1 is unsatisfiable, F2 is valid | |

F1 and F2 are both satisfiable |

Question 3 Explanation:

Question 4 |

Consider the following two statements :

S1: {0^{2n}|n\geq 1|} is a regular language

S2 : {0^{m}1^{n}0^{m+n}|m\geq 1 and n\geq 1|} is a regular language

Which of the following statements is correct?

S1: {0^{2n}|n\geq 1|} is a regular language

S2 : {0^{m}1^{n}0^{m+n}|m\geq 1 and n\geq 1|} is a regular language

Which of the following statements is correct?

Only S1 is correct | |

Only S2 is correct | |

Both S1 and S2 are correct | |

None of S1 and S2 is correct |

Question 4 Explanation:

Question 5 |

Which of the following statements true ?

If a language is context free it can be always be accepted by a deterministic
push-down automaton. | |

The union of two context free language is context free. | |

The intersection of two context free language is context free | |

The complement of a context free language is context free |

Question 5 Explanation:

There are 5 questions to complete.