RELATION AND FUNCTION

✤ Relation: Any subset of A × B is called relation from A to B

R ⊂ A × B.

2. Total number of relations = 2m × n

Here n(A) = m, n(B) = n.

3. Let R = {(x, a) (y, b) (z, c)} then domain is {x, y, z}

Range is {a, b, c}

4. If A and B has n element in common then A × B and B × A

has n² element in common.

5. If A = ∅ or B = ∅ then A × B = ∅

✤ Function: It is a rule by which elements of domain relate to elements

of co-domain.

It is represented by f: A → B.

Here A = domain, B = co-domain.

7. Every function is a relation but every relation is not a

function.

8. Domain : These are the Values of x for which polynomial

become Real.

Condition to find domain:

1. In square root, -ve should not occurs.

2. In denominator. zero should not occurs.

Conditions for being a function:

1. Every element of domain should have single image in Co-domain

2. In domain no element remain empty.

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