## Relation Formulas for Class 11

Here we are providing Relation Formula For Class 11 Maths. Practice **Relation **problems based on these formulas. Important terms and definitions are also included so that you can revise them in a very short time.

**List of Relation Formulas for Class 11**

(1) **Ordered Pair:** An ordered pair consists of two objects or elements grouped in a particular order.

Two numbers a and b listed in a specific order and enclosed in parentheses form an ordered pair (a, b) . Here a is the first component and b is the second component. In general, (a, b)≠(b, a) .

(2) **Equality of Ordered Pairs: **Two ordered pairs (a_{1}, b_{1}) and (a_{2}, b_{2}) are equal iff a_{1}=a_{2} and b_{1}=b_{2}

(a, b) = (c, d) ⇔ a = c and b = d.

(3) **Cartesian (or Cross) Product of Sets:**

For two non-empty sets A and B, the set of all ordered pairs (a, b) such that a ∈ A and b ∈ B is called Cartesian product A × B, i.e. A × B = {(a, b) : a ∈ A and b ∈ B}

If A = Φ or B = Φ then A x B = Φ

(4) **Ordered Triplet: **Three numbers a, b, c listed in a specific order and enclosed in parentheses form an ordered triplet (a, b, c).

(a, b, c) ≠ (b, a, c) ≠ (c, a, b), etc.

A× B×C = {(a, b, c) : a ∈ A, b ∈ B and c ∈ C}

(5) For any nonempty sets A, B, C, we have

(A x B) x C = A x (B x C), each denoted by A x B x C.

(6) *For any sets A, B and C, we have:*

(i) A x (B ∪ C) = (A x B) ∪ (A x C)

(ii) A x (B ∩ C) = (A x B) ∩ (A x C)

(iii) A x (B – C) = (A x B) – (A x C)

(iv) (A x B) ∩ (B x A) = (A ∩ B) x (B ∩ A) = (A ∩ B) x (A ∩ B)

(v) A x B = A x C ⇒ B = C

(vi) A ⊂ B ⇒ (A x A) ⊂ (A x B) ∩ (B x A)

(vii) A ⊂ B ⇒ (A x C) ⊂ (B x C)

(viii) A ⊂ B and C ⊂ D ⇒ (A x C) ⊂ (B x D)

(ix) A x B = B x A ⇔ A = B

(7) Let A and B be two nonempty sets and let R ⊆ A x B. Then, R is called a relation from A to B.

>> If (a, b) ∈ R, we say that ‘a is related to b‘ and we write, a R b.

>> If (a, b) ∉ R, we say that ‘a is not related to b‘

>> Dom (R) = {a : (a, b) ∈ R}, range (R) = {b : (a, b) ∈ R} .

(8) We define, R^{-1} = {(b, a) : (a, b) ∈ R},

dom (R) = range (R^{-1}) and range (R) = dom (R^{-1}).

(9) Let A be a nonempty set. Then, every subset of A x A is called a binary relation on A.

(10) If either A or B is an infinite set, then A × B is an infinite set.

(11) n(A × B) = n(A) × n(B)

(12) If A and B be any two non-empty sets having n elements in common, then A × B and B × A have n^{2} elements in common.