ABSTRACT ALGEBRA TEST

Let a binary operation ‘*’ be defined on a set A. The operation will be commutative if ________

• 
  a*b=b*a

• (b ο c)*a=(b*a) ο (c*a)

• (a*b)*c=a*(b*c)

• a*b=a

Let be a binary operation on N defined by ab=a-b+ab², then find 4*5.

• 9

• 98

• 88

• 99

Let ‘&’ be a binary operation defined on the set N. Which of the following definitions is commutative but not associative?

• a & b=a-b

• a & b=ab – 8

• 
  a & b=a+b

• 
  a & b=ab

Let ‘*’ be a binary operation defined by a*b=4ab. Find (a*b)*a.

• 
  4a² b

• 16ab²

• 16a² b

• 4ab²

Consider the binary operations on X, a*b = a+b+4, for a, b ∈ X. It satisfies the properties of _______.

• NOT A GROUP

• ABELIAN GROUP

• GROUP

In a group there must be only __________ identity element.

• 1

• 2

• 3

• 5

Which of the following multiplication tables defined on the set G={a,b,c,d} form a group?

• 
• 
• 
• 

When a function is one to one and onto, the function is said to be __________.

• bijective

• injective

• surjective

• 
  subjective

The sets R, Q, Z, 2Z with the usual addition have identity element which is 0. What is the inverse element of these sets for any element (a)?

• 0

• a

• 1

• -a

Set  Q  contains the letters in the word  SISTER .
 Which of the following is set  Q ?

• Q = { S, T, R }

• Q = { S, I, S, T, E, R }

• Q = { I, E }

• Q = { S, I, T, E, R }