1. Fill in the blanks with the SHORTEST string of characters so that the resultant
proposition is valid. [20]
(
2. State each of the following formulas
in English, if it is a wff. If it is not a wff, then give a reason why it is not a wff.
Here means likes and means
and the universe is the set of people: [15]
(a)
Everyone likes someone.
(b)
Someone likes everyone else.
(c)
Not a wff. can not be an argument of .
(d)
If someone likes everyone, then someone likes someone.
(e)
Not a wff. cannot be an argument of .
3 (a) Express the argument given below using the symbol suggested for each proposition. [8]
(b) Check whether or not the reasoning is correct using inference rules on the wffs (symbolic form) of (a).
[15]
Argument: If A took the laptop (A) or B lied (B), then a crime was committed (C).
If a crime was committed, then D must have been in town (D). But D
was not in town. Therefore, A did not take the laptop.
(a)
----------------
(b)
Reasoning is correct because:
----------------
(Modus Tollens)
----------------
(Modus Tollens)
from by De Morgan.
Hence from
by simplification.
4. Express the assertions given below as a proposition of a predicate logic using
the following predicates. The universe is the set of objects.[20]
: likes .
: is a lion.
: is a person.
: is strong.
(a) Everyone likes a (any) lion if it is strong.
, which is equivalent to
(b) Some strong lion likes only people.
(c) Sam likes a (some) lion.
(d) Some person likes a (any) lion only if it is strong.
(e) Not everyone likes a (any) lion.
5. Find the power set of each of the following sets: [7]
(a) {} :
(b) :
{ }
(c) { , {}} :
{
6. Indicate which of the following are true and which are false. [15]
(a) {
False
(b)
True
(c)
True
(d)
False
(e)
True