Mathematical Foundations of Computer Science Mid - I, September - 2010

1.(p→q) ↔(pq)isa
  • Tautology
  • Contradiction
  • Contingency
  • Contra positive
Answer: A
2.The disjunctive normal form of p (pq)is
  • p∨q
  • (p∧q) (p¬∨∧¬p)
  • (p∧q) (p∨∧¬p)
  • ¬pq
Answer: C
3.The contra positive of the statement ‘If n is a multiple of 12, then it is a multiple of 4 is
  • If n is a multiple of 4, then it is a multiple of 12
  • If n is not a multiple of 4, then it is not a multiple of 12
  • If n is not a multiple of 12, then it is not a multiple of 4.
  • If n not is a multiple of 4, then it is a multiple of 12.
Answer: B
4.The universe is the set of integers. The open statements are
p ( x ) : x is a perfect square. q ( x ) : x 5 is even 2
Which one is a true statement among the following.
  • (p( 4 ) ∨ q ( 5 ) )
  • (p( 4 ) q ( 6 ) )
  • (p( 6) ∨ q ( 4 ) )
  • (p( 9 ) q ( 8 ) )
Answer: A
5.p V q∨r
 � r
The conclusion of this valid argument is
  • p ∨q
  • q ∨r
  • ¬p ∨q
  • ¬r V p
Answer: A
6.If the number of elements in the set A is 2 and in B is 3, then the number of relations that can be formed fromAtoBis
  • 32
  • 16
  • 64
  • 128
Answer: C
7.The Hasse diagram for [1,2, 3,6] a b if and only if a divides b. is

  • image not found.
  • image not found.
  • image not found.
  • image not found.
Answer: C
8.If f= Z to Z , f(x) = 2x 1, then f is
  • A function but not one- one
  • One- one and onto function
  • One- one but not onto
  • Onto but not one- one
Answer: C
9.The additive set of integers mod 5 is a
  • Only semi group
  • Not a binary operation
  • Only monoid
  • A group
Answer: D
10.The order of 8 in the group of addition modulo 12 is
  • 3
  • 5
  • 7
  • 10
Answer: A
11.(pq) ∧ (pq) is equivalent to _______________
Answer: p V q
12.If the last column of the truth table consists of T entries, then the proposition is a _______________
Answer: Tautology
13.p;- Mohan is healthy q;- Mohan will go to the school contrapositive of p→q is ___________
Answer: If Mohan will not go to the school, then he is not healthy.
14.The argument (P- q) r →→
r �
_________ ∴ p ∧ �q
Is valid according to______________
Answer: Modus Tollens
15.p qr →∧
r �
_______
The conclusion according to addition and Demorgan is _____________
Answer: ¬ p
16.If A= ( 2, 3, 6, 12, 24 ), a b if and only if a divides b, then the number of edges of the Hasse diagram of (A, ) is ____________
Answer: 4
17.A relation R is compatible if it is ______________
Answer: Reflexive and Symmetric
18.If the number of elements in the set A is 5 and in B is 2, then the number of relations that can be formed from A to B is ________________
Answer: 1024
19.The order of –i in the group of 4th roots of unity is_____________
Answer: 4
20.The order the identity element of a group G is _____________
Answer: 1