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:

1. Reflexivity: Since a – a = 0 and 0 is an integer, this shows that (a, a) is in the relation; thus, proving R is reflexive.
2. 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.