![$[P \vee Q] \Leftrightarrow [\framebox[1.0in]{? }\rightarrow Q$](img1.gif){kind=small}
] (b)
![$[ \neg P \vee [\neg Q \vee R ] ] \Leftrightarrow [\framebox[1.0in] {?}\rightarrow R$](img2.gif){kind=small}
] (c)
![$\neg[P \rightarrow \framebox[1.0in]{? } ] \Leftrightarrow [P \wedge \neg Q$](img3.gif){kind=small}
]
(d)
![$[[P \vee \neg Q] \wedge R] \Leftrightarrow [[P \wedge R] \vee \framebox[1.0in]{? } $](img4.gif){kind=small}
]
(e)
![$[ [P \rightarrow Q ] \wedge \framebox[1.0in]{? } ] \Rightarrow \neg P$](img5.gif){kind=small}
1. Express the assertions given below as a proposition of a predicate logic using the following predicates. The universe is the set of objects.[25]
F(x): x is a fun.
M(x): x is a mathematics course.
P(x): x is a person.
L(x,y ): x likes y.
(a) Not everyone likes a mathematics course.
(b) Everyone likes a mathematics course if it is a fun.
(c) Everyone likes some mathematics courses.
(d) Some people like a mathematics course only if it is a fun.
(e) Some people like only mathematics courses.
2. Fill in the blanks with the shortest string of characters so that the resultant proposition is valid. [25]
(a)
]
(b)
]
(c)
]
(d)
]
(e)
3. Negate each of the propositions given below in English. Give a form other than simply putting 
in front. [8]
(1) If it is below freezing, it is also snowing.
(2) It is snowing only if it is below freezing.
(3) Someone has visited every country in the world.
(4) Every student in this class has taken exactly two math courses at this school.
4. Find the converse and the contrapositive of the following statements.
State them in English.[24]
(1) If it is below freezing, it is also snowing.
(2) It is snowing only if it is below freezing.
(3) It is necessary for taking this course that one has taken at least two
mathematics courses.
(4) It can not be true that everyone is rich and everyone is happy.
5(a) Express the argument given below using the symbol indicated for each proposition. [5]
(b) Using the symbols of (a) for the propositions, explain how the reasoning proceeds i.e.
identify each application of inference rule in the argument.
What conclusion do you draw ? Give your reasons. [13]
Argument:
If Macrohard takes over the browser market(M), then Orange takes over the PC market (O)
or NBM takes over the PC market (N).
If Outtel takes over the chip market(C), then NBM can not take over the PC market.
If Orange takes over the PC market, then Macrohard can not take over the browser market.
Macrohard has taken over the browser market and Outtel has taken over the chip market.