Advertisements
Advertisements
Question
The binary operation *: R x R → R is defined as a *b = 2a + b Find (2 * 3)*4
Advertisements
Solution
Given a*b = 2a + b
(2*3)*4 = (4 + 3)*4
= 7*4
= 14 + 4 =18
APPEARS IN
RELATED QUESTIONS
Let A = {1, 2, 3,......, 9} and R be the relation in A × A defined by (a, b) R (c, d) if a + d = b + c for (a, b), (c, d) in A × A. Prove that R is an equivalence relation. Also, obtain the equivalence class [(2, 5)].
Check whether the relation R in R defined by R = {(a, b) : a ≤ b3} is reflexive, symmetric or transitive.
Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.
Let R be the relation in the set N given by R = {(a, b) : a = b – 2, b > 6}. Choose the correct answer.
Let S be a relation on the set R of all real numbers defined by
S = {(a, b) ∈ R × R : a2 + b2 = 1}
Prove that S is not an equivalence relation on R.
Let R be the relation over the set of all straight lines in a plane such that l1 R l2 ⇔ l 1⊥ l2. Then, R is _____________ .
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 ______________ .
Show that the relation R on the set Z of all integers, given by R = {(a,b) : 2 divides (a-b)} is an equivalence relation.
If A = {a, b, c}, B = (x , y} find A × A.
The following defines a relation on N:
x is greater than y, x, y ∈ N
Determine which of the above relations are reflexive, symmetric and transitive.
Let A = {1, 2, 3} and consider the relation R = {1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1,3)}. Then R is ______.
Let the relation R be defined in N by aRb if 2a + 3b = 30. Then R = ______.
A relation R in set A = {1, 2, 3} is defined as R = {(1, 1), (1, 2), (2, 2), (3, 3)}. Which of the following ordered pair in R shall be removed to make it an equivalence relation in A?
A general election of Lok Sabha is a gigantic exercise. About 911 million people were eligible to vote and voter turnout was about 67%, the highest ever

Let I be the set of all citizens of India who were eligible to exercise their voting right in the general election held in 2019. A relation ‘R’ is defined on I as follows:
R = {(V1, V2) ∶ V1, V2 ∈ I and both use their voting right in the general election - 2019}
- Mr. Shyam exercised his voting right in General Election-2019, then Mr. Shyam is related to which of the following?
Students of Grade 9, planned to plant saplings along straight lines, parallel to each other to one side of the playground ensuring that they had enough play area. Let us assume that they planted one of the rows of the saplings along the line y = x − 4. Let L be the set of all lines which are parallel on the ground and R be a relation on L.
Answer the following using the above information.
- Let R = `{ ("L"_1, "L"_2) ∶ "L"_1 bot "L"_2 "where" "L"_1, "L"_2 in "L" }` which of the following is true?
A relation 'R' in a set 'A' is called a universal relation, if each element of' A' is related to :-
Let a set A = A1 ∪ A2 ∪ ... ∪ Ak, where Ai ∩ Aj = Φ for i ≠ j, 1 ≤ i, j ≤ k. Define the relation R from A to A by R = {(x, y): y ∈ Ai if and only if x ∈ Ai, 1 ≤ i ≤ k}. Then, R is ______.
What should be checked to determine whether a relation is transitive?
