Midterm Exam

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

• 1

• a

• -a

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

• Q = { S, T, R }
• Q = { I, E }
• Q = { S, I, S, T, E, R }
• Q = { S, I, T, E, R }

How many subsets will this set have? A= {a, b, c} ?

• 8

• 6

• 3

• 0

• 1

• 3

• 4

• 5

When can you say that two groups are isomorphic?

• Groups are isomorphic when they are homomorphic and bijective.

• Groups are isomorphic when they are automorphic and bijective.

• Groups are isomorphic when they are automorphic and surjective.

• Groups are isomorphic when they are homomorphic and bijective.

In using the Cayley Table, what is the identity element if you are working with group operation addition for a group of integers?

• 0

• 1

• i

• -1

What are the elements of the group Z/3Z?

• 1, 2, 3

• 0, 1, 2

• 0, 1, -1

• 1, i, -1

Which of the following is a group under multiplication?

• The set of integers

• The set of all rational numbers

• The set of all real numbers

• The set of all nonzero rational numbers

If (G, .) is a group such that a²=e , for all a∈G, then G is

• semigroup

• abelian group

• non-abelian group

• none of these

Which of the following is not a group property?

• It should have an identity element.

• It should be commutative.

• It should be symmetric.

• It should be associative.