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MIDTERM EXAMINATION

Fall 2011

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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

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 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

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 º ~p Ú q º ~(p Ù ~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 is

► One to one function

► Bijective Function

► Not well defined

Question No: 10 ( Marks: 1 ) - Please choose one

If f(x)=2x+1, then

► 4x-3

► 4x+3

Question No: 11 ( Marks: 1 ) - Please choose one

If f(x)=2x+1, then

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

Question No: 14 ( Marks: 1 ) - Please choose one

If f(x)= x+1 and g(x)= then (2f - 1g)x=

► 3x+2

Question No: 15 ( Marks: 1 ) - Please choose one

The Common fraction for the recurring decimal 0.81 is

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

► 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 È (B È C) = (A È B) È C

► A Ç (B Ç C) = (A Ç B) Ç C

► A È (B Ç C) = (A È B) Ç (A È 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

Question No: 21 ( Marks: 1 ) - Please choose one

In the given Venn diagram shaded area represents:

► (A Ç B) È C

► (A È Bc) È C

► (AÇ Bc) È Cc

► (A Ç B) Ç Cc

Question No: 22 ( Marks: 1 ) - Please choose one

For sets A, B and the universal set U, is equal to:

Question No: 23 ( Marks: 1 ) - Please choose one

A statement that certain objects belong to set is

► Recursion

► Base

► Restriction

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 .That is, find P().

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.

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)?

where

&

Solution:

► ~ (pq)

► ~ pq

► ~ pq

► None of these