Q. 1

# Let A and B be two nonempty sets.

(i) What do you mean by a relation from A to B?

(ii) What do you mean by the domain and range of a relation?

Answer :

(i) If A and B are two nonempty sets, then any subset of the set (A × B) is said to a relation R from set A to set B.

That means, if R be a relation from A to B then R ⊆ (A × B).

Therefore, (x, y) R ⇒ (x, y) (A × B)

That means x is in relation to y. Or we can write xRy.

(ii) Let R be a relation from A to B. Then, the set containing all the first elements of the ordered pairs belonging to R is called Domain.

For the relation R, Dom(R) = {x: (x, y) R}

And the set containing all the second elements of the ordered pair belonging to R is called Range.

For the relation R, Range(R) = {y: (x, y) R}

Rate this question :

State True or False for the following statements

If (x – 2, y + 5) = are two equal ordered pairs, then x = 4, .

Mathematics - ExemplarIf [x]^{2} – 5 [x] + 6 = 0, where [ . ] denote the greatest integer function, then

A. x ∈ [3, 4]

B. x ∈ (2, 3]

C. x ∈ [2, 3]

D. x ∈ [2, 4)

Mathematics - ExemplarState True or False for the following statements

The ordered pair (5, 2) belongs to the relation R = {(x, y) : y = x – 5, x, y ∈ **Z**}

Let A = {3, 4, 5, 6} and R = {(a, b) : a, b ϵ A and a <b

(i) Write R in roster form.

(ii) Find: dom (R) and range (R)

(iii) Write R^{–1} in roster form

RS Aggarwal - Mathematics

Let R = {(a, b) : a, b, ϵ N and a < b}.

Show that R is a binary relation on N, which is neither reflexive nor symmetric. Show that R is transitive.

RS Aggarwal - Mathematics

Let A = (1, 2, 3} and B = {4}

How many relations can be defined from A to B.

RS Aggarwal - Mathematics

Is the given relation a function? Give reasons for your answer.

t = {(x, 3) | x is a real number.

Mathematics - ExemplarLet R = {(x, y): x, y ϵ Z and x^{2} + y^{2} ≤ 4}.

(i) Write R in roster form.

(ii) Find dom (R) and range (R).

RS Aggarwal - Mathematics

Let f : R^{+} → R : f(x) = log_{e} x. Find {x : f(x) = –2}.