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TOPICS
Formulae
Relations :-
```1. Reflexive, if (a, a) ∈ R, for every a ∈ A
2. Symmetric, if (a, b) ∈ R implies that (b, a) ∈ R, for every (a, b) ∈ A
3. Transitive, if (a, b) ∈ R and (b, c) ∈ R implies that (a, c) ∈ R, for all (a, b, c) ∈ A.
4. Equivalence, if Reflexive, Symmetric, and Transitive Relation.
```
Functions :-
```1. One-to-One or Injective, for every x₁, x₂ ∈ X, f(x₁) = f(x₂) implies x₁ = x₂.
2. On-to or Surjective,  for every y ∈ Y, there exists an element x in X such that f(x) = y.
3. Bijetive, if Injective and Surjective function.
```
Composition :-
```1. Composite, gof(x) = g(f(x))
2. Composite, fog(x) = f(g(x))
3. Composite, fof(x) = f(f(x))
4. Invertible, f(x) = ax + b, then put f(x) = y, find value of x = ? i.e., f-1(y) is a inverse value of x.
```
Binary :-
```1. Commutative, if a + b = b + a and a x b = b x a for every a, b ∈ X.
2. Associative, if (a + b) + c = a + (b + c) and (a x b) x c = a x (b x c) for every a, b, c ∈ X.
3. Identity, if e ∈ a then a ∗ e = a = e ∗ a, ∀ a ∈ A.
4. Invertible, if e ∈ a then a ∗ b = e = b ∗ a, ∀ a ∈ A i.e., a-1
```
CLASSES