Midterm Examination s5

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?

► 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

► ~ (pq)

► ~ pq

► ~ pq

► 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:

► ~ (pq)

► ~ pq

► ~ pq

► 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:

► ~ (pq)

► ~ pq

► ~ pq

► None of these

Question No: 27 ( Marks: 10 ) For the real valued functions are defined below

Find gof(x) and gog(x)?

f( x )= 3 x4 - 2 x 2

2 & g( x ) = x

Solution:

► ~ (pq)

► ~ pq

► ~ pq

► None of these