If (x + 1, 1) = (3y, y - 1), find the values of x and y.

If the ordered pairs (x, - 1) and (5, y) belong to the set {(a, b): b = 2a - 3}, find the values of x and y.

If a ∈ { - 1, 2, 3, 4, 5} and b ∈ {0, 3, 6}, write the set of all ordered pairs (a, b) such that a + b = 5.

If a ∈ {2, 4, 6, 9} and b ∈{4, 6, 18, 27}, then form the set of all ordered pairs (a, b) such that a divides b and a<b.

If A = {1, 2} and B = {1, 3}, find A x B and B x A.

Let A = {1, 2, 3} and B = {3, 4}. Find A x B and show it graphically

If A = {1, 2, 3} and B = {2, 4}, what are A x B, B x A, A x A, B x B, and (A x B) ∩ (B x A)?

If A and B are two sets having 3 elements in common. If n(A) = 5, n(B) = 4, find n(A x B) and n[(A x B) ∩ (B x A)].

Let A and B be two sets. Show that the sets A x B and B x A have an element in common if the sets A and B be two sets such that n (A) = 3 and n (B) = 2.

Let A and B be two sets such that n(A) x B, find A and B, where x, y, z are distinct elements

Let A = {1, 2, 3, 4} and R = {(a, b): a ∈ A, b ∈ A, a divides b}. Write R explicitly.

If A = { - 1, 1}, find A x A x A.

State whether each of the following statements are true of false. If the statement is false, re - write the given statement correctly:

i. If P = [m, n} and Q = {n, m} then P x Q = {(m, n), (n, m)}

ii. If A and B are non - empty sets, then A x B is a non - empty set of ordered pairs (x, y) such that x ∈ B and y ∈ A.

iii. If A = {1, 2}, B]{3, 4}, then A x (B ∩ φ) = φ.

If A = {1, 2}, form the set A x A x A.

If A = {1, 2, 4} and B = {1, 2, 3}, represent following sets graphically:

i. A x B ii. B x A

iii A x A iv. B x B

Given A = {1, 2, 3}, B = {3, 4}, C = {4, 5, 6}, find (A x B) ∩ (B x C).

If A = {2, 3}, B = {4, 5}, C = {5, 6} find A x (B ∪ C), (A x B) ∪ (A x C).

If A = {1, 2, 3}, B = {4}, c = {5}, then verify that:

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).

Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that:

i. A x C B x D

ii. A x (B ∩ C) = (A x B) ∩ (A x C)

If A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}, find

i. A x (B ∩ C)

ii. (A x B) ∩ (A xC)

iii. A x (B ∪ C)

iv. (A x B) ∪ (A x C)

Prove that:

(A ∪ B) x C = (A x C) = (A x C) ∪ (B x C)

Prove that:

(A ∩ B) x C = (A x C) ∩ (B x C)

If A x B ⊆ C x D and A ∩ B ∈ ∅, Prove that A ⊆ C and B ⊆ D.

If A = {1, 2, 3}, B = {4, 5, 6}, which of the following are relations from A to B?

Give reasons in support of your answer.

A relation R is defined from a set A = {2, 3, 4, 5} to a set B = {3, 6, 7, 10} as follows: (x, y) R x is relatively prime to y. Express R as a set of ordered pairs and determine its domain and range.

Let A be the set of first five natural and let R be a relation on A defined as follows: (x, y) R x ≤ y

Express R and R^-1 as sets of ordered pairs. Determine also

i. the domain of R^‑1

ii. The Range of R.

Find the inverse relation R^-1 in each of the following cases:

i. R= {(1, 2), (1, 3), (2, 3), (3, 2), (5, 6)}

ii. R= {(x, y) : x, y N; x + 2y = 8}

iii. R is a relation from {11, 12, 13} to (8, 10, 12} defined by y = x – 3

Write the following relations as the sets of ordered pairs:

A relation R from the set {2, 3, 4, 5, 6} to the set {1, 2, 3} defined by x = 2y.

Write the following relations as the sets of ordered pairs:

A relation R on the set {1,2,3,4,5,6,7} defined by

(x, y) R x is relatively prime to y.

Write the following relations as the sets of ordered pairs:

A relation R on the set {0,1,2,…,10} defined by

2x + 3y = 12.

Write the following relations as the sets of ordered pairs:

A relation R form a set A = {5, 6, 7, 8} to the set B = {10, 12, 15, 16, 18} defined by (x, y) R x divides y.

Let R be a relation in N defined by (x, y) R x + 2y = 8. Express R and R^-1 as sets of ordered pairs.

Let A = {3, 5} and B = {7, 11}. Let R = {(a, b): a A, b B, a-b is odd}. Show that R is an empty relation from into B.

Let A = {1, 2} and B={3, 4}. Find the total number of relations from A into B.

Determine the domain and range of the relation R defined by

R = {(x, x+5): x {0, 1, 2, 3, 4, 5}

Determine the domain and range of the relation R defined by

R= {(x, x³): x is a prime number less than 10}

Determine the domain and range of the following relations:

R= {a, b): a N, a < 5, b = 4}

Determine the domain and range of the following relations:

S= {a, b): b = |a-1|, a Z and |a| ≤ 3}

Let A = {a, b}. List all relations on A and find their number.

Let A= {x, y, z} and B= {a, b}. Find the total number of relations from A into B.

Let R be a relation from N to N defined by R= {(a, b): a, b N and a = b²}.

Are the following statements true?

i. (a, a) R for all a N

ii. (a, b) R (b, a) R

iii. (a, b) R and (b, c) R (a, c) R

Let A= {1, 2, 3,….,14}. Define a relation on a set A by R= {(x, y): 3x – y = 0, where x, y A}. Depict this relationship using an arrow diagram. Write down its domain, co-domain and range.

Define a relation R on the set N of natural numbers by R = {(x, y): y = x + 5, x is a natural less than 4, x, y N}.Depict this relationship using (i) roster form an arrow diagram. Write down the domain and range of R.

A = {1, 2, 3, 5} and B = {4, 6, 9}. Define a relation R from A to B by R = {(x, y): the difference between x and y is odd, x A, y B}. Write R in Roster form.

Write the relation R = {(x, x³): x is a prime number less than 10} in roster form.

Let A= {1, 2, 3, 4, 5, 6}. Let R be a relation on A defined by

R= {(a, b): a, b A, b is exactly divisible by a}

i. Write R in roster form

ii. Find the domain of R

iii. Find the range of R.

Figure 2.15 shows a relationship between the sets P and Q. Write this relation in

a. Set builder form

b. Roster form

c. What is its domain and range?

Let R be the relation on Z defined by R = {(a, b) Z, a – b is an integer}. Find the domain and range of R.

For the relation R₁ defined on R by the rule (a, b) R₁ 1 + ab > 0. Prove that: (a, b) R₁ and (b,c) R₁ (a, c) R₁ is not true for all a, b, c R.

Let R be a relation on N x N defined by (a, b) R (c, d) a + d = b + c for all (a, b), (c, d) N x N.

Show that:

i. (a, b) R (a, b) for all (a, b) N x N

ii. (a, b) R (c, d) (c, d) R (a, b) for all (a, b), (c, d) N x N

iii. (a, b) R (c, d) and (c, d) R (e, f) (a, b) R (e, f) for all (a, b), (c, d), (e, f) N × N

If A = {1, 2, 4}, B = {2, 4, 5} and C = {2, 5}, write (A − C) × (B − C).

If n(A) = 3, n(B) = 4, ten write n (A × A × B).

If R = {(x, y) : x, yZ, x² + y²≤ 4} is a relation defined on the set Z of integers, then write domain of R.

If R is a relation from set A = {11, 12, 13} to set B = {8, 10, 12} defined by y = x − 3, the write R⁻¹.

Let A = {1, 2, 3} and R = {(a, b) : | a²− b² | ≤5, a, b A}. Then write R as set of ordered pairs.

Let R = {(x, y) : x, y Z, y = 2x − 4}. If (a, −2) and (4, b²)R, then write the values of a and b.

If R = {(2, 1), (4, 7), (1, −2), ...}, then write the linear relation between the components of the ordered pairs of the relation R.

If A = {1, 3, 5} and B = {2, 4}, list the elements of R, if R = {(x, y) : x, yA × B and x > y}.

If R = {(x, y) : x, yW, 2x + y = 8}, then write the domain and range of R.

Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1), (y, 2), (z, 1) are in A × B, write A and B.

Let A = {1, 2, 3, 5}, B = {4, 6, 9} and R be a relation from A to B defined by R = {(x, y) : x − y is odd}. Write R in roster form.

Mark the correct alternative in the following:

If A = {1, 2, 4}, B = {2, 4, 5}, C = {2, 5}, then (A−B) × (B − C) is

Mark the correct alternative in the following:

If R is a relation on the set A = {1, 2, 3, 4, 5, 6, 7, 9} given by xRyy = 3 x, then R =

Mark the correct alternative in the following:

Let A = {1, 2, 3}, B = {1, 3, 5}. If relation R and A to B is given by R = {(1, 3), (2, 5), (3, 3)}. Then R⁻¹ is

Mark the correct alternative in the following:

If A = {1, 2, 3} B = {1, 4, 6, 9} and R is a relation from A to B defined by ‘x is greater than y. The range of R is

Mark the correct alternative in the following:

If R = {(x, y) :x, yZ, x² + y²≤ 4} is a relation on Z, then domain of R is

Mark the correct alternative in the following:

A relation R is defined from {2, 3, 4, 5} to {3, 6, 7, 10} by :xRyx is relatively prime to is relatively prime to y. Then, domain of R is

Mark the correct alternative in the following:

A relation φ from C to R is defined by xφy |x| = y. Which one is correct?

Mark the correct alternative in the following:

Let R be a relation on N defined by x + 2 y = 8. The domain of R is

Mark the correct alternative in the following:

R is a relation from {11, 12, 13} to {8, 10, 12} defined by y = x− 3. Then, R⁻¹ is

Mark the correct alternative in the following:

If the set A has p elements, B has q elements, then the number of elements in A ×B is

Mark the correct alternative in the following:

Let R be a relation from a set A to a set B, then

Mark the correct alternative in the following:

If R is a relation from a finite set A having m elements to a finite set B having n elements, then the number of relations from A to B is

Mark the correct alternative in the following:

If R is a relation on a finite set having n elements, then the number of relations on A is