Question

List the members of the equivalence relation on {1,2,3,4}. Find the equivalence classes [1],[2],[3],[4] for the followi

{{1},{2},{3},{4}}

Determine whether each relation is reflexive,antisymmetric , or transitive

(x,y) in R if xy>1

(x,y) in R if x > y

(x,y) in R if 3 divides x + 2y

Answer 1

The given partition is {{1},{2},{3},{4}}.

Members of the equivalence relation:

It is the process of taking the all possible mappings within an individual set element.

Members of the equivalence relation of {{1},{2},{3},{4}}:

Since there is single element in each so it maps to itself.

(1, 1), (2, 2), (3, 3), (4, 4)

Equivalence class:

If a relation is equivalence then it has equivalent classes.

Condition [a] = {x∈X|xRa}

where a is an element and X is the set.

Find the equivalence class [1]:

Since single element (1,1) so equivalence class is {1}.

Find the equivalence class [2]:

Since single element (2,2) so equivalence class is {2}

Find the equivalence class [3]:

Since single element (3,3) so equivalence class is {3}

Find the equivalence class [4]:

Since single element (4,4) so equivalence class is {4}

According to HOMEWORKLIB RULES i have to solve first question only