Advertisements
Advertisements
Question
Given A = {1, 2, 3, 4, 5}, S = {(x, y) : x ∈ A, y ∈ A}. Find the ordered pairs which satisfy the conditions given below:
x + y > 8
Solution
A = {1, 2, 3, 4, 5}, S = {(x, y) : x ∈ A, y ∈ A}
x + y > 8
So, we find the ordered pair such that x + y > 8
Where x and y belongs to set A = {1, 2, 3, 4, 5}
1 + 1 = 2 < 8
1 + 2 = 3 < 8
1 + 3 = 4 < 8
1 + 4 = 5 < 8
1 + 5 = 6 < 8
2 + 1 = 3 < 8
2 + 2 = 4 < 8
2 + 3 = 5 < 8
2 + 4 = 6 < 8
2 + 5 = 7 < 8
3 + 1 = 4 < 8
3 + 2 = 5 < 8
3 + 3 = 6 < 8
3 + 4 = 7 < 8
3 + 5 = 8
4 + 1 = < 8
4 + 2 = 6 < 8
4 + 3 = 7 < 8
4 + 4 = 8
4 + 5 = 9 > 8
So one of the ordered pairs is (4, 5)
5 + 1 = 6 < 8
5 + 2 = 7 < 8
5 + 3 = 8
5 + 4 = 9>8
So one of the ordered pairs is (5, 4)
5 + 5 = 10 > 8
So one of the ordered pairs is (5, 5)
Therefore, the set of ordered pairs satisfying x + y > 8 = {(4, 5), (5, 4), (5, 5)}.
APPEARS IN
RELATED QUESTIONS
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.
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, find A and B, where x, y, z are distinct elements.
State whether of the statement is true or false. If the statement is false, re-write the given statement correctly:
If A and B are non-empty sets, then A × B is a non-empty set of ordered pairs (x, y) such that x ∈ B and y ∈ A.
Let A be the set of first five natural numbers 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.
Write the relation as the sets of ordered pairs:
(ii) 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 relation as the sets of ordered pairs:
(iii) A relation R on the set [0, 1, 2, ....., 10] defined by 2x + 3y = 12.
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 = {1, 2, 3} and\[R = \left\{ \left( a, b \right) : \left| a^2 - b^2 \right| \leq 5, a, b \in A \right\}\].Then write R as set of ordered pairs.
If R = {(2, 1), (4, 7), (1, −2), ...}, then write the linear relation between the components of the ordered pairs of the relation R.
Write the following relations as sets of ordered pairs and find which of them are functions:
(b) {(x, y) : y > x + 1, x = 1, 2 and y = 2, 4, 6}
Write the following relations as sets of ordered pairs and find which of them are functions:
{(x, y) : x + y = 3, x, y, ∈ [0, 1, 2, 3]}
Express the function f : X → R given by f(x) = x3 + 1 as set of ordered pairs, where X = {−1, 0, 3, 9, 7}
If `(x/3+1, y-2/3)` = `(5/3,1/3),`find the values of x and y.
Given A = {1, 2, 3, 4, 5}, S = {(x, y) : x ∈ A, y ∈ A}. Find the ordered pairs which satisfy the conditions given below:
x + y = 5
Express the following functions as set of ordered pairs and determine their range.
f : X → R, f(x) = x3 + 1, where X = {–1, 0, 3, 9, 7}
State True or False for the following statement.
The ordered pair (5, 2) belongs to the relation R = {(x, y) : y = x – 5, x, y ∈ Z}.
