मराठी

Mark the Correct Alternative in the Following Question: 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 _______________ .

Advertisements
Advertisements

प्रश्न

Mark the correct alternative in the following question:

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 _______________ .

पर्याय

  • reflexive but not symmetric

  • reflexive but not transitive

  • symmetric and transitive

  • neither symmetric nor transitive

MCQ
Advertisements

उत्तर

We have,

R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)}

Hence, R is reflexive but not symmetric

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Relations - Exercise 1.4 [पृष्ठ ३३]

APPEARS IN

आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
पाठ 1 Relations
Exercise 1.4 | Q 27 | पृष्ठ ३३

संबंधित प्रश्‍न

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

Relation R in the set A = {1, 2, 3, 4, 5, 6} as R = {(x, y) : y is divisible by x}.


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

Relation R in the set Z of all integers defined as R = {(x, y) : x – y is an integer}.


Show that the relation R in R defined as R = {(a, b) : a ≤ b}, is reflexive and transitive but not symmetric.


Let A be the set of all human beings in a town at a particular time. Determine whether the following relation is reflexive, symmetric and transitive:

R = {(x, y) : x and y live in the same locality}


The following relation is defined on the set of real numbers.
aRb if a – b > 0

Find whether relation is reflexive, symmetric or transitive.


Give an example of a relation which is symmetric but neither reflexive nor transitive?


Defines a relation on N:

x + 4y = 10, x, y ∈ N

Determine the above relation is reflexive, symmetric and transitive.


Prove that the relation R on Z defined by
(a, b) ∈ R ⇔ a − b is divisible by 5
is an equivalence relation on Z.


Let O be the origin. We define a relation between two points P and Q in a plane if OP = OQ. Show that the relation, so defined is an equivalence relation.


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.


If R = {(x, y) : x2 + y2 ≤ 4; x, y ∈ Z} is a relation on Z, write the domain of R.


Write the identity relation on set A = {a, b, c}.


Let A = {3, 5, 7}, B = {2, 6, 10} and R be a relation from A to B defined by R = {(x, y) : x and y are relatively prime}. Then, write R and R−1.


Define an equivalence relation ?


A = {1, 2, 3, 4, 5, 6, 7, 8} and if R = {(xy) : y is one half of xxy ∈ A} is a relation on A, then write R as a set of ordered pairs.


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 _______________ .


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 ______________ .


Let R = {(a, a), (b, b), (c, c), (a, b)} be a relation on set A = a, b, c. Then, R is _______________ .


If R is a relation on the set A = {1, 2, 3, 4, 5, 6, 7, 8, 9} given by x R y ⇔ y = 3 x, then R = _____________ .


Mark the correct alternative in the following question:

The relation S defined on the set R of all real number by the rule aSb if a  b is _______________ .


Mark the correct alternative in the following question:

Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as aRb if a is congruent to b for all a, b  T. Then, R is ____________ .


Show that the relation R on the set Z of integers, given by R = {(a,b):2divides (a - b)} is an equivalence relation. 


If `f(x) = (4x + 3)/(6x - 4), x ≠ 2/3`, show that fof (x) = x for all `x ≠ 2/3`. Also, find the inverse of f.


Show that the relation R on R defined as R = {(a, b): a ≤ b}, is reflexive, and transitive but not symmetric.


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


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


In the set of natural numbers N, define a relation R as follows: ∀ n, m ∈ N, nRm if on division by 5 each of the integers n and m leaves the remainder less than 5, i.e. one of the numbers 0, 1, 2, 3 and 4. Show that R is equivalence relation. Also, obtain the pairwise disjoint subsets determined by R


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


Let S = {1, 2, 3, 4, 5} and let A = S x S. Define the relation R on A as follows:
(a, b) R (c, d) iff ad = cb. Then, R is ____________.


Let R be the relation “is congruent to” on the set of all triangles in a plane is ____________.


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


Let the relation R in the set A = {x ∈ Z : 0 ≤ x ≤ 12}, given by R = {(a, b) : |a – b| is a multiple of 4}. Then [1], the equivalence class containing 1, is:


Given triangles with sides T1: 3, 4, 5; T2: 5, 12, 13; T3: 6, 8, 10; T4: 4, 7, 9 and a relation R inset of triangles defined as R = `{(Delta_1, Delta_2) : Delta_1  "is similar to"  Delta_2}`. Which triangles belong to the same equivalence class?


A relation S in the set of real numbers is defined as `"xSy" => "x" - "y" + sqrt3`  is an irrational number, then relation S 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


If f(x + 2a) = f(x – 2a), then f(x) is:


Let R1 and R2 be two relations defined as follows :

R1 = {(a, b) ∈ R2 : a2 + b2 ∈ Q} and

R2 = {(a, b) ∈ R2 : a2 + b2 ∉ Q}, where Q is the set of all rational numbers. Then ______


lf A = {x ∈ z+ : x < 10 and x is a multiple of 3 or 4}, where z+ is the set of positive integers, then the total number of symmetric relations on A is ______.


Let A = {3, 5}. Then number of reflexive relations on A is ______.


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)

Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×