Advertisements
Advertisements
प्रश्न
The binary operation *: R x R → R is defined as a *b = 2a + b Find (2 * 3)*4
उत्तर
Given a*b = 2a + b
(2*3)*4 = (4 + 3)*4
= 7*4
= 14 + 4 =18
APPEARS IN
संबंधित प्रश्न
determination of whether the following relations are reflexive, symmetric, and transitive:
Relation R in the set Z of all integers defined as
R = {(x, y): x − y is an integer}
Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as R = {(a, b): b = a + 1} is reflexive, symmetric, or transitive.
Show that the relation R in the set A = {1, 2, 3, 4, 5} given by R = {(a, b) : |a - b| is even}, is an equivalence relation. Show that all the elements of {1, 3, 5} are related to each other and all the elements of {2, 4} are related to each other. But no element of {1, 3, 5} is related to any element of {2, 4}.
Given an example of a relation. Which is Transitive but neither reflexive nor symmetric.
Given an example of a relation. Which is Reflexive and transitive but not symmetric.
If A = {1, 2, 3, 4} define relations on A which have properties of being reflexive, symmetric and transitive ?
An integer m is said to be related to another integer n if m is a multiple of n. Check if the relation is symmetric, reflexive and transitive.
Give an example of a relation which is reflexive and transitive but not symmetric ?
Defines a relation on N :
xy is square of an integer, x, y ∈ N
Determine the above relation is reflexive, symmetric and transitive.
Let L be the set of all lines in XY-plane and R be the relation in L defined as R = {L1, L2) : L1 is parallel to L2}. Show that R is an equivalence relation. Find the set of all lines related to the line y= 2x + 4.
A = {1, 2, 3, 4, 5, 6, 7, 8} and if R = {(x, y) : y is one half of x; x, y ∈ A} is a relation on A, then write R as a set of ordered pairs.
If A = {a, b, c}, then the relation R = {(b, c)} on A is _______________ .
Let A = {2, 3, 4, 5, ..., 17, 18}. Let '≃' be the equivalence relation on A × A, cartesian product of Awith itself, defined by (a, b) ≃ (c, d) if ad = bc. Then, the number of ordered pairs of the equivalence class of (3, 2) is _______________ .
A relation ϕ from C to R is defined by x ϕ y ⇔ | x | = y. Which one is correct?
Show that the relation R on R defined as R = {(a, b): a ≤ b}, is reflexive, and transitive but not symmetric.
If A = {1, 2, 3, 4 }, define relations on A which have properties of being:
reflexive, symmetric and transitive
Given A = {2, 3, 4}, B = {2, 5, 6, 7}. Construct an example of the following:
a mapping from A to B which is not injective
The following defines a relation on N:
x y is square of an integer x, y ∈ N
Determine which of the above relations are reflexive, symmetric and transitive.
Consider the non-empty set consisting of children in a family and a relation R defined as aRb if a is brother of b. Then R is ______.
The relation R on the set A = {1, 2, 3} defined as R = {{1, 1), (1, 2), (2, 1), (3, 3)} is reflexive, symmetric and transitive.
R = {(1, 1), (2, 2), (1, 2), (2, 1), (2, 3)} be a relation on A, then R is ____________.
Let A = {1, 2, 3}. Which of the following is not an equivalence relation on A?
A relation R on a non – empty set A is an equivalence relation if it is ____________.
Let us define a relation R in R as aRb if a ≥ b. Then R is ____________.
Let R be a relation on the set N of natural numbers denoted by nRm ⇔ n is a factor of m (i.e. n | m). Then, R is ____________.
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}
- The above-defined relation R is ____________.
The value of k for which the system of equations x + ky + 3z = 0, 4x + 3y + kz = 0, 2x + y + 2z = 0 has nontrivial solution is
If A is a finite set consisting of n elements, then the number of reflexive relations on A is
In a group of 52 persons, 16 drink tea but not coffee, while 33 drink tea. How many persons drink coffee but not tea?
The number of surjective functions from A to B where A = {1, 2, 3, 4} and B = {a, b} is