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Quiz on Equivalence Relation

Authored by Latha Latha

Mathematics

12th Grade

Used 4+ times

Quiz on Equivalence Relation
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8 questions

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1.

MULTIPLE CHOICE QUESTION

1 min • 2 pts

Empty relations defined on a non-empty set are ____.

not reflexive

symmetric

transitive

all the above

Answer explanation

Media Image

Empty relations on a non-empty set are always not reflexive, but symmetric and transitive.

2.

FILL IN THE BLANK QUESTION

1 min • 2 pts

Let S = {1,2,3} and ρ = {(1,1),(1,2),(2,2),(1,3),(3,1)}. Write the ordered pair(s) to be included to make S symmetric.

Answer explanation

A relation is said to symmetric if for every (a,b) in the relation must have (b,a) also. Here (1,2) is present but (2,1) is not present. So not symmetric.

3.

MULTIPLE CHOICE QUESTION

1 min • 2 pts

Smallest equivalence relation formed using the set A={1,2,3} is AXA.

True
False

Answer explanation

Smallest equivalence relation formed using the set A={1,2,3} is {(1,1), (2,2), (3,3)}.
AXA is the largest equivalence relation on A.

4.

MULTIPLE CHOICE QUESTION

1 min • 2 pts

Let S = {1,2,3} and ρ = {(1,1),(1,2),(2,2),(1,3),(3,1),(3,3), (2,1),(2,3),(3,2)}. Then ρ is ___.

not reflexive

not symmetric

not transitive

equivalence

Answer explanation

Equivalence.

5.

MULTIPLE CHOICE QUESTION

1 min • 2 pts

Media Image

(1)

(2)

(3)

(4)

Answer explanation

Media Image

6.

MULTIPLE CHOICE QUESTION

1 min • 2 pts

Which of the following is a property of an equivalence relation?

It is reflexive

It is antisymmetric

It is irreflexive

It is asymmetric

7.

MULTIPLE CHOICE QUESTION

1 min • 2 pts

For the set B = {a,b,c}, the relation R = {(a,a),(b,b),(c,c),(a,b),(b,c)} is ___.

an equivalence relation

not reflexive

not symmetric

not transitive

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