मराठी

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

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प्रश्न

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

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उत्तर

Given a*b = 2a + b

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

= 7*4

= 14 + 4 =18

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2017-2018 (March) Set 1

संबंधित प्रश्‍न

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.


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


If A = {2, 3, 4}, B = {1, 3, 7} and R = {(x, y) : x ∈ A, y ∈ B and x < y} is a relation from A to B, then write R−1.


State the reason for the relation R on the set {1, 2, 3} given by R = {(1, 2), (2, 1)} to be transitive ?


Let the relation R be defined on N by aRb iff 2a + 3b = 30. Then write R as a set of ordered pairs


Write the smallest equivalence relation on the set A = {1, 2, 3} ?


The relation R = {(1, 1), (2, 2), (3, 3)} on the set {1, 2, 3} is ___________________ .


Mark the correct alternative in the following question:

For real numbers x and y, define xRy if `x-y+sqrt2` is an irrational number. Then the relation R is ___________ .


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


Let A = {1, 2, 3, 4}, B = {4, 5, 6}, C = {5, 6}. Find A × (B ∪ C).


Write the relation in the Roster form and hence find its domain and range:

R2 = `{("a", 1/"a")  "/"  0 < "a" ≤ 5, "a" ∈ "N"}`


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


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?


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 ____________.

On the set N of all natural numbers, define the relation R by a R b, if GCD of a and b is 2. Then, R is


Given a non-empty set X, define the relation R in P(X) as follows:

For A, B ∈ P(X), (4, B) ∈ R iff A ⊂ B. Prove that R is reflexive, transitive and not symmetric.


Read the following passage:

An organization conducted bike race under two different categories – Boys and Girls. There were 28 participants in all. 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} and G = {g1, g2}, where B represents the set of Boys selected and G the set of Girls selected for the final race.

Based on the above information, answer the following questions:

  1. How many relations are possible from B to G? (1)
  2. Among all the possible relations from B to G, how many functions can be formed from B to G? (1)
  3. Let R : B `rightarrow` B be defined by R = {(x, y) : x and y are students of the same sex}. Check if R is an equivalence relation. (2)
    OR
    A function f : B `rightarrow` G be defined by f = {(b1, g1), (b2, g2), (b3, g1)}. Check if f is bijective. Justify your answer. (2)

Which relation is called an Empty Relation?


What should be checked to determine whether a relation is reflexive?


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