MIDTERM EXAMINATION
Fall 2009
MTH202- Discrete Mathematics
Question No: 1 ( Marks: 1 ) - Please choose one
The inverse of given relation R = {(1,1),(1,2),(1,4),(3,4),(4,1)} is
► {(1,1),(2,1),(4,1),(2,3)}
► {(1,1),(1,2),(4,1),( 4,3),(1,4)}
► {(1,1),(2,1),(4,1),(4,3),(1,4)}
Question No: 2 ( Marks: 1 ) - Please choose one
Symmetric and antisymmetric are
► Negative of each other
► Both are same
► Not negative of each other
Question No: 3 ( Marks: 1 ) - Please choose one
Let A = {a, b, c} and
R = {(a, c), (b, b), (c, a)} be a relation on A. Is R
► Transitive
► Reflexive
► Symmetric
► Transitive and Reflexive
Question No: 4 ( Marks: 1 ) - Please choose one
Let A= {1, 2, 3, 4} and R = {(1, 1), (2, 2), (3, 3),(4,4)} then
► R is symmetric.
► R is anti symmetric.
► R is transitive.
► R is reflexive.
► All given options are true
Question No: 5 ( Marks: 1 ) - Please choose one
The contrapositive of the conditional statement p q is
► ~p ~q
► q p
► ~q 
~p
~p
► None of these
Question No: 6 ( Marks: 1 ) - Please choose one
In Boolean addition 1+1=
► 2
► 1
► 0
Question No: 7 ( Marks: 1 ) - Please choose one
The negation of “Today is Friday” is
► Today is Saturday
► Today is not Friday
► Today is Thursday
Question No: 8 ( Marks: 1 ) - Please choose one
The same element can never appear twice in a set.
► True
► False
Question No: 9 ( Marks: 1 ) - Please choose one
If f(x)=2x+1, 
then fg(x)=
then fg(x)=
► 
► 
► 
Question No: 10 ( Marks: 1 ) - Please choose one
The statement p q ~p q ~(p ~q)
describes
► Commutative Law
► Implication Laws
► Exportation Law
► Equivalence
Question No: 11 ( Marks: 1 ) - Please choose one
If two sets are not equal, then one must be a subset of the other
► True
► False
Question No: 12 ( Marks: 1 ) - Please choose one
If f and g are two one-to-one functions then their composition that is gof is
► Not one-to-one
► Onto
► One-to-one
► Onto and one-to-one
Question No: 13 ( Marks: 1 ) - Please choose one
If a set contains exactly m distinct elements where m denotes some non negative integer then the set is .
► Finite
► Infinite
► None of these
Question No: 14 ( Marks: 1 ) - Please choose one
If f(4) = 1 and g(1) = 4 then fog(1) =
► 3
► 1
► 4
Question No: 15 ( Marks: 1 ) - Please choose one
If (
) = A, then (
) = B
) = A, then () = B
► True
► False
► Cannot be determined
Question No: 16 ( Marks: 1 ) - Please choose one
The total number of elements in a set is called
► Strength
► Cardinality
► Finite
Question No: 17 ( Marks: 1 ) - Please choose one
If f(x) = x and g(x)=-2x then (f+g)x =
► 3x
► 
► –x
Question No: 18 ( Marks: 1 ) - Please choose one
Associative law of Intersection for three sets
► A (B C) = (A B) C
► A 
(B C) = (A B) C
(B C) = (A B) C
► A (B C) = (A B) (A B)
► None of these
Question No: 19 ( Marks: 1 ) - Please choose one
Which term of the sequence 4,1,-2,… is -77
► 26
► 27
► 28
Question No: 20 ( Marks: 1 ) - Please choose one
If a set A has 5 elements then power set of A. P(S) contains elements. Which are?
► 
► 
► 
► 
Question No: 21 ( Marks: 1 ) - Please choose one
A collection of rules indicating how to form new set objects from those already known to be in the set is called
► Base
► Restriction
► Recursion
Question No: 22 ( Marks: 1 ) - Please choose one
is
► Arithmetic series
Arithmetic series
► Geometric series
► Arithmetic sequence
► Geometric sequence
Question No: 23 ( Marks: 1 ) - Please choose one
► 4
► 3
► -2
Question No: 24 ( Marks: 1 ) - Please choose one
The product of the positive integers from 1 to n is called
► Multiplication
► n factorial
► Geometric sequence
Question No: 25 ( Marks: 3 )
Consider the geometric progression 5/7, 5/49, 5/343, …
· Identify r
· Find the nth term of this progression
· If the above progression is to be added up to infinite terms then what could be the sum?
Answer:-
nth term=?
Sum=?
As 
So, formula is:-
Question No: 26 ( Marks: 5 )
Determine whether the following statement is tautology or not (use truth table)
p
|
q
|
~p
|
~q
|  |
~q
 | |
1
|
1
|
0
|
0
|
1
|
1
|
0
|
1
|
0
|
0
|
1
|
1
|
1
|
0
|
0
|
1
|
1
|
0
|
0
|
0
|
1
|
0
|
0
|
1
|
1
|
1
|
1
|
1
|
Hence, it is not a tautology as there are two false.
Question No: 27 ( Marks: 10 )
Write an input/output table for the circuit:
Input signals are:
X = 1
Y = 0
Z = 0
X
|
Y
|
Z
|
X^Y
|
(X^Y)
 Z |
~[(X^Y)
Z] |
1
|
0
|
0
|
0
|
0
|
1
|
__________________________________________________________
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