## Prepositional-Logic

Question 1 |

Let p and q be propositions. Using only the truth table decide whether p ⇔ q does not imply p → q is true or false.

True | |

False |

Question 1 Explanation:

So, "imply" is False making "does not imply" True.

Question 2 |

A language with string manipulation facilities uses the following operations

head(s): first character of a string tail(s): all but the first character of a string concat(s1,s2):s1 s2 for the string acbc what will be the output of concat(head(s), head(tail(tail(s))))

ac | |

bc | |

ab | |

cc |

Question 2 Explanation:

concat (a, head (tail (tail (acbc))))

concat (a, head (tail (cbc)))

concat (a, head (bc))

concat (a, b)

ab

concat (a, head (tail (cbc)))

concat (a, head (bc))

concat (a, b)

ab

Question 3 |

If the proposition ¬p ⇒ ν is true, then the truth value of the proposition ¬p ∨ (p ⇒ q), where ¬ is negation, ‘∨’ is inclusive or and ⇒ is implication, is

true | |

multiple valued | |

false | |

cannot be determined |

Question 3 Explanation:

From the axiom ¬p → q, we can conclude that p ∨ q.

So, either p or q must be True.

Now,

¬p ∨ (p → q)

= ¬p ∨ (¬p ∨ q)

= ¬p ∨ q

Since nothing c an be said about the truth values of p, it implies that ¬p ∨ q can also be True or False. Hence, the value cannot be determined.

So, either p or q must be True.

Now,

¬p ∨ (p → q)

= ¬p ∨ (¬p ∨ q)

= ¬p ∨ q

Since nothing c an be said about the truth values of p, it implies that ¬p ∨ q can also be True or False. Hence, the value cannot be determined.

Question 4 |

The proposition p ∧(~p ∨ q) is:

a tautology | |

logically equivalent to p ∧ q | |

logically equivalent to p ∨ q | |

a contradiction | |

none of the above |

Question 4 Explanation:

p ∧(~p ∨ q)

(p ∧ ~p) ∨ (p ∧ q)

F ∨ (p ∧ q)

(p ∧ q)

(p ∧ ~p) ∨ (p ∧ q)

F ∨ (p ∧ q)

(p ∧ q)

Question 5 |

Which of the following predicate calculus statements is/are valid:

a | |

b | |

c | |

d |

Question 5 Explanation:

(A) Valid

(B) Invalid

(C) Invalid

(D) Invalid

(B) Invalid

(C) Invalid

(D) Invalid

Question 6 |

Which of the following is/are tautology

a | |

b | |

c | |

d |

Question 6 Explanation: