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

f = {(x, x) | x is a real number}

State True or False for the following statements

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

If [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)

State 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

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.

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

How many relations can be defined from A to B.

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

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

Let R = {(x, y): x, y ϵ Z and x² + y² ≤ 4}.

(i) Write R in roster form.

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

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

Let A = {2, 3} and B= {3, 5}

(i) Find (A × B) and n(A × B).

(ii) How many relations can be defined from A to B?