ECAT Pre Engineering Mathematic MCQ Test With Answer for Chapter 2 (Set Function and Groups)

Z is the set of integers, (z, *) is a group with a * b = a + b + 1, a, b∈G. then inverse of a is

• -a A
• a + 1 B
• -2 -a C
• None of these D

• 
  A
• 
  B
• 
  C
• 
  D

If n(X) = 18, n(X∩Y) = 7, n(X∪ Y) = 40 then n(Y) =

• 1 A
• 12 B
• 5 C
• 29 D

If p and q are two statements then their biconditional 'p if q' is denoted by

• 
  A
• 
  B
• 
  C
• 
  D

A conjunction of two statement p and q is true only if

• p is true A
• q is true B
• Both p and q are true C
• both p and q are false D

A∪(A∪B)= --------------------

• B A
• A B
• A∪B C
• None of these D

A disjunction of two statement p and q is true

• p is false A
• q is false B
• Both p and q are false C
• One of p and q is true D

The set (Z,+) forms a group

• Forms a group w.r.t addition A
• Non commutative group w.r.t multiplication B
• Forms a group w.r.t multiplication C
• Doesn't form a group D

The statement that a group can have more than one identity elements is

• True A
• False B
• Ambiguous C
• Some times true D

The set {Z\ {0} } is group w.r.t

• Addition A
• Multiplication B
• Division C
• Subtraction D

• Addition A
• Subtraction B
• Multiplication C
• None of these D

• 
  A
• 
  B
• 
  C
• 
  D

The set {x +iy / x, y ∈ Q} forms a group under the binary operation of

• Addition A
• Multiplication B
• Division C
• Both addition and multiplication D

Which of the following is the definition of singleton

• The objects in a set A
• A set having no element B
• A set having no subset C
• None of these D

The statement that a group can have more than one identity elements is

• True A
• False B
• Fallacious C
• Some times true D

If we have a statement "if p then q" then q is called

• Conclusion A
• Implication B
• Unknown C
• Hypothesis D

• 
  A
• 
  B
• 
  C
• none of these D

• An empty set A
• Universal set B
• A singleton set C
• None of these D

If A⊆ B, and B is a finite set, then

• n (a) < n(B) A
• n(B)<(A) B
• n(A)≤ n (B) C
• n(A)≥ n(B) D

The sets {1, 2, 4} and {4, 6, 8, 10} are

• Equal sets A
• Equivalent sets B
• Disjoint sets C
• Over lapping sets D

P∉ A means

• Pis subset of A A
• Pis an element of A B
• P does not belongs to A C
• A does not element of P D

If A and B are two sets then any subset R of A x B is called

• relation on A A
• relation on B B
• relation from A to B C
• relation from B to A D

Which of the following is the subset of all sets?

• 
  A
• 
  B
• 
  C
• 
  D

The set of complex numbers forms a group under the binary operation of

• Addition A
• Multiplication B
• Division C
• Subtraction D

The set {Z\{0}} is group w.r.t

• Addition A
• Multiplication B
• Division C
• Subtraction D

The contra positive of p → q is

• q → p A
• ~q→~q B
• ~p→~q C
• None of these D

A = B iff

• All elements of A also the elements of B A
• A and B should be singleton B
• A and B have the same number of elements C
• If both have the same element D

The set of natural is a semi group w.r.t

• Addition A
• Division B
• Subtraction C
• None of these D

The set {-1,1} is

• Group under the multiplication A
• Group under addition B
• Does not form a group C
• Contains no identity element D

Write down the power set of {9, 11}

• 
  A
• 
  B
• 
  C
• 
  D