www.vuhelp.pk MIDTERM EXAMINATION Fall 2011 www.vuhelp.pk MTH202- Discrete Mathematics (Session - 1)
Question No: 1 ( Marks: 1 ) - Please choose one If p = It is raining
q = She will go to college
"It is raining and she will not go to college" will be denoted by
►
►
►
►
Question No: 2 ( Marks: 1 ) - Please choose one An arrangement of rows and columns that specifies the truth value of a compound proposition for all possible truth values of its constituent propositions is called
► Truth Table
► Venn diagram
► False Table
► None of these
Question No: 3 ( Marks: 1 ) - Please choose one www.vuhelp.pk 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 If two relations A and S are reflexive then A S must
► Symmetric
► Reflexive
► Transitive
Question No: 5 ( Marks: 1 ) - Please choose one Symmetric and antisymmetric are
► Negative of each other
► Both are same
► Not negative of each other
Question No: 6 ( Marks: 1 ) - Please choose one Inverse of relation can be obtained by
► changing signs of elements in order pairs
► changing position of elements in order pairs
► Taking multiplicative inverse of elements in order pairs www.vuhelp.pk Question No: 7 ( Marks: 1 ) - Please choose one The order pairs which are not present in a relation, must be present in
► Inverse of that relation
► Composition of relations
► Complementry relation of that relation
Question No: 8 ( Marks: 1 ) - Please choose one The statement p q ~p q ~(p ~q) describes
► Commutative Law
► Implication Laws
► Exportation Law
► Equivalence
Question No: 9 ( Marks: 1 ) - Please choose one
If f is a function from Z to R then f( n ) = n is
► One to one function
► Bijective Function
► Not well defined
Question No: 10 ( Marks: 1 ) - Please choose one
If f(x)=2x+1, g(x)=x2 -1 then f2 (x)= www.vuhelp.pk
► 4x-3
► 4x2 +1
► 4x+3
Question No: 11 ( Marks: 1 ) - Please choose one If f(x)=2x+1, g(x)=x2 -1then g2 (x)=
3 2 ► x -2x
4 2 ► x -2x
4 ► x +1
Question No: 12 ( Marks: 1 ) - Please choose one Let f and g be the functions defined by f(x)= 2x+3 & g(x)= 3x+2 then composition of f and g is
► 6x+6
► 5x+5
► 6x+7
Question No: 13 ( 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 www.vuhelp.pk
Question No: 14 ( Marks: 1 ) - Please choose one If f(x)= x+1 and g(x)= -2x2 + 1 then (2f - 1g)x=
► 2x2 - x
► 3x+2
► 2x2 + 2 x + 1
Question No: 15 ( Marks: 1 ) - Please choose one The Common fraction for the recurring decimal 0.81 is
81 ► 100
81 ► 98
9 ► 11
Question No: 16 ( Marks: 1 ) - Please choose one A recursive definition for a set consists of the following three rules
► Base, Recursion, Restriction
► Base, Boolean, Restriction
► Base, Recursion, index
► None of the above
Question No: 17 ( 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 www.vuhelp.pk ► Base
► Restriction
► Recursion
Question No: 18 ( Marks: 1 ) - Please choose one The power set of a set A is the set of all subsets of A, denoted P(A).
► True
► False
Question No: 19 ( Marks: 1 ) - Please choose one Associative law of Intersection for three sets
► A (B C) = (A B) C
► A (B C) = (A B) C
► A (B C) = (A B) (A B)
► None of these
Question No: 20 ( Marks: 1 ) - Please choose one What is the output state of an OR gate if the inputs are 0 and 1?
► 0
► 1
► 2
► 3 www.vuhelp.pk
Question No: 21 ( Marks: 1 ) - Please choose one In the given Venn diagram shaded area represents:
► (A B) C
► (A Bc) C
► Bc) Cc
► (A B) Cc
Question No: 22 ( Marks: 1 ) - Please choose one For sets A, B and the universal set U, (A B )c is equal to:
► Ac B c
► Ac B
► Ac B c
► A Bc
Question No: 23 ( Marks: 1 ) - Please choose one A statement that certain objects belong to set is
► Recursion
► Base
► Restriction www.vuhelp.pk
Question No: 24 ( Marks: 1 ) - Please choose one If p= A Pentium 4 computer,
q= attached with ups.
Then "no Pentium 4 computer is attached with ups" is denoted by
► ~ (pq)
► ~ pq
► ~ pq
► None of these
Question No: 25 ( Marks: 3 ) Suppose A={1}and B={u,v}.Find the power set of A B .That is, find P( A B ).
Solution:
► ~ (pq)
► ~ pq
► ~ pq
► None of these
Question No: 26 ( Marks: 5 ) The fifth term of an arithmetic sequence is 17 and ninth term is 37 find the first four terms of this sequence. www.vuhelp.pk
Solution:
► ~ (pq)
► ~ pq
► ~ pq
► None of these
Question No: 27 ( Marks: 10 ) For the real valued functions are defined below
Find gof(x) and gog(x)?
where
f( x )= 3 x4 - 2 x 2
2 & g( x ) = x
Solution:
► ~ (pq)
► ~ pq
► ~ pq
► None of these