# Mathematical Logic [GATE (Graduate Aptitude Test in Engineering) Computer Science]: Questions 1 - 3 of 84

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## Question 1

### Question MCQ▾

Which of the following arguments are not valid?

(1) “If Gora gets the job and works hard, then he will be promoted. If Gora gets promotion, then he will be happy. He will not be happy, therefore, either he will not get the job or he will not work hard” .

(2) “Either Puneet is not guilty or Pankaj is telling the truth. Pankaj is not telling the truth, therefore, Puneet is not guilty” .

(3) If n is a real number such that n > 1, then n^{2} > 1. Suppose that n^{2} > 1, then n > 1. (December)

### Choices

Choice (4) | Response | |
---|---|---|

a. | (1) and (2) | |

b. | Only (3) | |

c. | (1) , (2) and (3) | |

d. | Only (2) |

## Question 2

Appeared in Year: *2015*

### Question MCQ▾

Let P (m, n) be the statement “m divides n” where the Universe of discourse for both the variables is the set of positive integers. Determine the truth values of the following propositions.

(December)

### Choices

Choice (4) | Response | |
---|---|---|

a. | (1) -True; (2) -True; (3) -True | |

b. | (1) -True; (2) -False; (3) -False | |

c. | (1) -True; (2) -True; (3) -False | |

d. | (1) -False; (2) -False; (3) -False |

## Question 3

Appeared in Year: *2015*

### Question MCQ▾

Consider the compound propositions given below as:

Which of the above propositions are tautologies? (December)

### Choices

Choice (4) | Response | |
---|---|---|

a. | (1) and (3) | |

b. | (2) and (3) | |

c. | (1) and (2) | |

d. | (1) , (2) and (3) |