Engineering Mathematics - Set Theory and Algebra

Question - 1

What is the possible number of reflexive relations on a set of 5 elements?

  • A 210
  • B 215
  • C 220
  • D 225

Question - 2

Consider the set \(S=\left\{ 1,\omega ,{ \omega }^{ 2 } \right\} \) where \(\omega \) and \({ \omega }^{ 2 }\) are cube root of unity. If  * denotes the multiplication operations, the structure {S*} forms

  • A a group
  • B a ring
  • C an integral domain
  • D a field

Question - 3

Which one of the following is true for any simple connected undirected graph with more than two vertices?

  • A Commutativity
  • B Associativity
  • C Existence of inverse for every element
  • D Existence of identity

Question - 4

Which one of the following is true for any simple connected undirected graph with more than two vertices?

  • A No two vertices have the same degree
  • B Atleast two vertices have the same degree
  • C Atleast three vertices have the same degree
  • D All vertices have the same degree

Question - 5

Consider the binary relation R={(x,y), (x,z), (z,x), (z,y)} on the set {x,y,z} which one of the following is true?

  • A R is symmetric but not anti-symmetric
  • B R is not symmetric but anti-symmetric
  • C R is both symmetric and anti-symmetric
  • D R is neither symmetric nor anti-symmetric

Question - 6

If P,Q,R are subset of the universal set U, then \(\left( P\cap Q\cap R \right) \cup \left( { P }^{ c }\cap Q\cap R \right) \cup { Q }^{ c }\cup { R }^{ c }\) is

  • A \({ Q }^{ c }\cup { R }^{ c }\)
  • B \(P\cup { Q }^{ c }\cup { R }^{ c }\)
  • C \({ P }^{ c }\cup { Q }^{ c }\cup { R }^{ c }\)
  • D \(\cup \)

Question - 7

Let S be a set of n elements. The number of ordered pairs in the largest and the smallest equivalence relations on S are

  • A n and n
  • B n2 and n
  • C n and 0
  • D n and 1

Question - 8

Let X,Y,Z be sets of sizes X,Y and Z respectively. Let W=XxY and E be the set of all subsets of W. The number of functions from Z to E is

  • A Z
  • B Zx2xy
  • C Z2
  • D 2xyz

Question - 9

The set {1,2,3,5,7,8,9} under multiplication modulo 10 is not a group. Given below are four plausible reasons. Which one of them is false?

  • A It is not closed
  • B 2 does not have an inverse
  • C 3 does not have an inverse
  • D 8 does not have an inverse

Question - 10

Which one of the following option is CORRECT given three positive integers x,y and z and a predicate

  • A P(x) being true means that x is a prime number
  • B P(x) being true means that x is a number other than 1
  • C P(x) is always true irrespective of the value of x
  • D P(x) is being true means that x has exactly two factors other than 1 and x
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