<p>www.vuhelp.pk MIDTERM EXAMINATION Fall 2011 www.vuhelp.pk MTH202- Discrete Mathematics (Session - 1) </p><p>Question No: 1 ( Marks: 1 ) - Please choose one If p = It is raining</p><p> q = She will go to college</p><p>"It is raining and she will not go to college" will be denoted by </p><p>► </p><p>► </p><p>► </p><p>► </p><p>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 </p><p>► Truth Table</p><p>► Venn diagram</p><p>► False Table</p><p>► None of these</p><p>Question No: 3 ( Marks: 1 ) - Please choose one www.vuhelp.pk Let A = {a, b, c} and </p><p>R = {(a, c), (b, b), (c, a)} be a relation on A. Is R</p><p>► Transitive</p><p>► Reflexive</p><p>► Symmetric </p><p>► Transitive and Reflexive</p><p>Question No: 4 ( Marks: 1 ) - Please choose one If two relations A and S are reflexive then A S must </p><p>► Symmetric</p><p>► Reflexive</p><p>► Transitive</p><p>Question No: 5 ( Marks: 1 ) - Please choose one Symmetric and antisymmetric are</p><p>► Negative of each other</p><p>► Both are same</p><p>► Not negative of each other</p><p>Question No: 6 ( Marks: 1 ) - Please choose one Inverse of relation can be obtained by</p><p>► changing signs of elements in order pairs</p><p>► changing position of elements in order pairs</p><p>► 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 </p><p>► Inverse of that relation</p><p>► Composition of relations</p><p>► Complementry relation of that relation</p><p>Question No: 8 ( Marks: 1 ) - Please choose one The statement p q  ~p  q  ~(p  ~q) describes </p><p>► Commutative Law</p><p>► Implication Laws</p><p>► Exportation Law</p><p>► Equivalence</p><p>Question No: 9 ( Marks: 1 ) - Please choose one</p><p>If f is a function from Z to R then f( n ) = n is</p><p>► One to one function</p><p>► Bijective Function</p><p>► Not well defined</p><p>Question No: 10 ( Marks: 1 ) - Please choose one</p><p>If f(x)=2x+1, g(x)=x2 -1 then f2 (x)= www.vuhelp.pk</p><p>► 4x-3 </p><p>► 4x2 +1</p><p>► 4x+3</p><p>Question No: 11 ( Marks: 1 ) - Please choose one If f(x)=2x+1, g(x)=x2 -1then g2 (x)=</p><p>3 2 ► x -2x</p><p>4 2 ► x -2x</p><p>4 ► x +1</p><p>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</p><p>► 6x+6</p><p>► 5x+5</p><p>► 6x+7</p><p>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</p><p>► Not one-to-one </p><p>► Onto</p><p>► One-to-one </p><p>► Onto and one-to-one www.vuhelp.pk</p><p>Question No: 14 ( Marks: 1 ) - Please choose one If f(x)= x+1 and g(x)= -2x2 + 1 then (2f - 1g)x=</p><p>► 2x2 - x</p><p>► 3x+2</p><p>► 2x2 + 2 x + 1</p><p>Question No: 15 ( Marks: 1 ) - Please choose one The Common fraction for the recurring decimal 0.81 is</p><p>81 ► 100</p><p>81 ► 98</p><p>9 ► 11</p><p>Question No: 16 ( Marks: 1 ) - Please choose one A recursive definition for a set consists of the following three rules</p><p>► Base, Recursion, Restriction</p><p>► Base, Boolean, Restriction</p><p>► Base, Recursion, index</p><p>► None of the above </p><p>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</p><p>► Restriction</p><p>► Recursion</p><p>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).</p><p>► True </p><p>► False</p><p>Question No: 19 ( Marks: 1 ) - Please choose one Associative law of Intersection for three sets </p><p>► A  (B  C) = (A  B)  C</p><p>► A  (B  C) = (A  B)  C</p><p>► A  (B  C) = (A  B)  (A  B)</p><p>► None of these</p><p>Question No: 20 ( Marks: 1 ) - Please choose one What is the output state of an OR gate if the inputs are 0 and 1?</p><p>► 0</p><p>► 1</p><p>► 2</p><p>► 3 www.vuhelp.pk</p><p>Question No: 21 ( Marks: 1 ) - Please choose one In the given Venn diagram shaded area represents:</p><p>► (A  B)  C</p><p>► (A  Bc)  C</p><p>►  Bc)  Cc</p><p>► (A  B)  Cc</p><p>Question No: 22 ( Marks: 1 ) - Please choose one For sets A, B and the universal set U, (A B )c is equal to:</p><p>► Ac B c</p><p>► Ac B</p><p>► Ac B c</p><p>► A Bc</p><p>Question No: 23 ( Marks: 1 ) - Please choose one A statement that certain objects belong to set is </p><p>► Recursion</p><p>► Base</p><p>► Restriction www.vuhelp.pk</p><p>Question No: 24 ( Marks: 1 ) - Please choose one If p= A Pentium 4 computer,</p><p> q= attached with ups.</p><p>Then "no Pentium 4 computer is attached with ups" is denoted by</p><p>► ~ (pq)</p><p>► ~ pq</p><p>► ~ pq</p><p>► None of these</p><p>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 ).</p><p>Solution: </p><p>► ~ (pq)</p><p>► ~ pq</p><p>► ~ pq</p><p>► None of these</p><p>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</p><p>Solution: </p><p>► ~ (pq)</p><p>► ~ pq</p><p>► ~ pq</p><p>► None of these</p><p>Question No: 27 ( Marks: 10 ) For the real valued functions are defined below</p><p>Find gof(x) and gog(x)?</p><p> where</p><p> f( x )= 3 x4 - 2 x 2</p><p>2 & g( x ) = x</p><p>Solution: </p><p>► ~ (pq)</p><p>► ~ pq</p><p>► ~ pq</p><p>► None of these</p>