Equivalence Relation Quiz

Give an example of an equivalence relation in real life.

• The relation of 'being taller than'

• The relation of 'having a different eye color than'

• The relation of 'having the same birthday as'

• The relation of 'being born in a different country than'

Define an equivalence relation and provide an example to illustrate it.

• Red, blue, and green

• Reflexive, symmetric, and transitive

• Additive, subtractive, and multiplicative

• Monday, Tuesday, and Wednesday

Explain why 'equality' is an equivalence relation.

• Equality is not an equivalence relation.

• Equality is only reflexive and symmetric, not transitive.

• Equality is reflexive, symmetric, and transitive.

• Equality is not reflexive, symmetric, or transitive.

Provide an example of an equivalence relation on the set of integers.

• Congruence modulo n

• Greater than relation

• Addition relation

• Divisibility relation

Discuss the concept of 'equivalence classes' with an example.

• Equivalence classes are sets that group together elements that are only partially related.

• Equivalence classes are sets that group together elements that are considered equivalent under a certain relation.

• Equivalence classes are sets that group together elements that are randomly selected.

• Equivalence classes are sets that group together elements that are completely unrelated.

Explain how 'congruence modulo n' is an equivalence relation.

• Congruence modulo n is an equivalence relation because it satisfies addition, subtraction, and multiplication.

• Congruence modulo n is an equivalence relation because it only satisfies reflexivity.

• Congruence modulo n is an equivalence relation because it satisfies reflexivity, symmetry, and transitivity.

• Congruence modulo n is an equivalence relation because it is not related to any other mathematical concept.

Give an example of an equivalence relation on the set of all triangles.

• Having the same area

• Having the same perimeter

• Having the same number of sides

• Having the same color

Discuss the concept of 'partition' in relation to equivalence relations.

• Creating overlapping subsets

• Combining all elements into one subset

• Division of a set into disjoint subsets

• Arranging the elements in ascending order

Explain why 'similarity' is an equivalence relation in geometry.

• Similarity is an equivalence relation because it involves parallel lines

• Similarity is an equivalence relation because it involves right angles

• In geometry, 'similarity' is an equivalence relation because it satisfies the properties of reflexive, symmetric, and transitive.

• Similarity is an equivalence relation because it involves congruent shapes

Provide an example of an equivalence relation in computer science.

• Greater than

• Not equal to

• Less than

• Equality