हिंदी

The Binary Operation *: R X R → R Is Defined as a *B = 2a + B Find (2 * 3)*4 - Mathematics

Advertisements
Advertisements

प्रश्न

The binary operation *: R x R → R is defined as a *b = 2a + b Find (2 * 3)*4

Advertisements

उत्तर

Given a*b = 2a + b

(2*3)*4 = (4 + 3)*4

= 7*4

= 14 + 4 =18

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
2017-2018 (March) Set 1

संबंधित प्रश्न

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)].


Determine whether the following relation is reflexive, symmetric and transitive:

Relation R in the set A of human beings in a town at a particular time given by R = {(x, y) : x is exactly 7 cm taller than y}.


Show that the relation R in the set R of real numbers, defined as R = {(a, b) : a ≤ b2} is neither reflexive nor symmetric nor transitive.


Let A = {x ∈ Z : 0 ≤ x ≤ 12}. Show that R = {(ab) : a∈ A, |a – b| is divisible by 4}is an equivalence relation. Find the set of all elements related to 1. Also write the equivalence class [2]


If = {1, 2, 3, 4} define relations on A which have properties of being reflexive, transitive but not symmetric ?


If = {1, 2, 3, 4} define relations on A which have properties of being symmetric but neither reflexive nor transitive ?


If = {1, 2, 3, 4} define relations on A which have properties of being reflexive, symmetric and transitive ?


Give an example of a relation which is reflexive and transitive but not symmetric?


Let A = {abc} and the relation R be defined on A as follows: R = {(aa), (bc), (ab)}. Then, write minimum number of ordered pairs to be added in R to make it reflexive and transitive.


m is said to be related to n if m and n are integers and m − n is divisible by 13. Does this define an equivalence relation?


If R is a symmetric relation on a set A, then write a relation between R and R−1.


Let R = {(x, y) : |x2 − y2| <1) be a relation on set A = {1, 2, 3, 4, 5}. Write R as a set of ordered pairs.


Let A = {0, 1, 2, 3} and R be a relation on A defined as
R = {(0, 0), (0, 1), (0, 3), (1, 0), (1, 1), (2, 2), (3, 0), (3, 3)}
Is R reflexive? symmetric? transitive?


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


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


Mark the correct alternative in the following question:

The maximum number of equivalence relations on the set A = {1, 2, 3} is _______________ .


If A = {a, b, c}, B = (x , y} find A × B.


If A = {a, b, c}, B = (x , y} find B × B.


Let A = {a, b, c} and the relation R be defined on A as follows:
R = {(a, a), (b, c), (a, b)}.
Then, write minimum number of ordered pairs to be added in R to make R reflexive and transitive


Give an example of a map which is neither one-one nor onto


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 and also obtain the equivalent class [(2, 5)]


Total number of equivalence relations defined in the set S = {a, b, c} is ____________.


The relation R is defined on the set of natural numbers as {(a, b) : a = 2b}. Then, R-1 is given by ____________.


Given set A = {1, 2, 3} and a relation R = {(1, 2), (2, 1)}, the relation R will be ____________.


Given set A = {a, b, c}. An identity relation in set A 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}

  • Mr. Shyam exercised his voting right in General Election-2019, then Mr. Shyam is related to which of the following?

An organization conducted a bike race under 2 different categories-boys and girls. Totally there were 250 participants. Among all of them finally, three from Category 1 and two from Category 2 were selected for the final race. Ravi forms two sets B and G with these participants for his college project. Let B = {b1,b2,b3} G={g1,g2} where B represents the set of boys selected and G the set of girls who were selected for the final race.

Ravi decides to explore these sets for various types of relations and functions.

  • Let R: B → B be defined by R = {(x, y): x and y are students of same sex}, Then this 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


Let f(x)= ax2 + bx + c be such that f(1) = 3, f(–2) = λ and f(3) = 4. If f(0) + f(1) + f(–2) + f(3) = 14, then λ is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×