# What is equivalence class of a language?

## What is equivalence class of a language?

Equivalence Classes. Consider any regular language L. u ≡L w iff for all x, ux ∈ L iff wx ∈ L. Note that ≡L is indeed an equivalence relation, as it is reflexive, symmetric and transitive. Let equiv(w) denote the equivalence class of w.

**What do you mean by equivalence class with example?**

Examples of Equivalence Classes If X is the set of all integers, we can define the equivalence relation ~ by saying ‘a ~ b if and only if ( a – b ) is divisible by 9’. Then the equivalence class of 4 would include -32, -23, -14, -5, 4, 13, 22, and 31 (and a whole lot more).

### How many equivalence classes are there explain?

There are five distinct equivalence classes, modulo 5: [0], [1], [2], [3], and [4]. {x ∈ Z | x = 5k, for some integers k}. Definition 5. Suppose R is an equivalence relation on a set A and S is an equivalence class of R.

**What are equivalence classes in TOC?**

Other things about equivalence class is that, if x and y are two strings of same class( here reaching same state), and we append some strings z to then i.e, xz and yz, that will also reach to same equivalence class (either same or any other). Minimal DFA serve our purpose.

#### How do you show an equivalence class?

To prove an equivalence relation, you must show reflexivity, symmetry, and transitivity, so using our example above, we can say:

- Reflexivity: Since a – a = 0 and 0 is an integer, this shows that (a, a) is in the relation; thus, proving R is reflexive.
- Symmetry: If a – b is an integer, then b – a is also an integer.

**What is the equivalence class of 0?**

So the equivalence class of 0 is the set of all integers that we can divide by 3, i.e. that are multiples of 3:{…,−6,−3,0,3,6,…}. The set has the following equivalence relations.

## What are the equivalence classes of the equivalence relations in Exercise 3?

Since 0 and 3 are each only equivalent to themselves, while 1 and 2 are equivalent to each other, there are 3 equivalence classes and they are 10l,11,2l, and 13l.