हिंदी

Write the Smallest Reflexive Relation on Set a = {1, 2, 3, 4}.

Advertisements
Advertisements

प्रश्न

Write the smallest reflexive relation on set A = {1, 2, 3, 4}.

एक पंक्ति में उत्तर
योग
Advertisements

उत्तर

Here,
A = {1, 2, 3, 4}
Also, a relation is reflexive iff every element of the set is related to itself.

So, the smallest reflexive relation on the set A is
R = {(1, 1), (2, 2), (3, 3), (4, 4)}

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Relations - Exercise 1.3 [पृष्ठ ३०]

APPEARS IN

आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
अध्याय 1 Relations
Exercise 1.3 | Q 4 | पृष्ठ ३०

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 the set A = {x ∈ Z : 0 ≤ x ≤ 12} given by R = {(a, b) : |a – b| is a multiple of 4} is an equivalence relation. Find the set of all elements related to 1.


Given an example of a relation. Which is reflexive and symmetric but not transitive.


Given an example of a relation. Which is reflexive and transitive but not symmetric.


Let A = {1, 2, 3}. Then number of equivalence relations containing (1, 2) is ______.


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


Test whether the following relation R1 is  (i) reflexive (ii) symmetric and (iii) transitive :

R1 on Q0 defined by (a, b) ∈ R1 ⇔ = 1/b.


Let A = {1, 2, 3}, and let R1 = {(1, 1), (1, 3), (3, 1), (2, 2), (2, 1), (3, 3)}, R2 = {(2, 2), (3, 1), (1, 3)}, R3 = {(1, 3), (3, 3)}. Find whether or not each of the relations R1, R2, R3 on A is (i) reflexive (ii) symmetric (iii) transitive.


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


Let R be the relation defined on the set A = {1, 2, 3, 4, 5, 6, 7} by R = {(a, b) : both a and b are either odd or even}. Show that R is an equivalence relation. Further, show that all the elements of the subset {1, 3, 5, 7} are related to each other and all the elements of the subset {2, 4, 6} are related to each other, but no element of the subset {1, 3, 5, 7} is related to any element of the subset {2, 4, 6}.


If R and S are relations on a set A, then prove that R and S are symmetric ⇒ R ∩ S and R ∪ S are symmetric ?


If R = {(x, y) : x + 2y = 8} is a relation on N by, then write the range of R.


Define a transitive relation ?


If A = {3, 5, 7} and B = {2, 4, 9} and R is a relation given by "is less than", write R as a set ordered pairs.


Let R be the equivalence relation on the set Z of the integers given by R = { (ab) : 2 divides }.

Write the equivalence class [0].


For the set A = {1, 2, 3}, define a relation R on the set A as follows:
R = {(1, 1), (2, 2), (3, 3), (1, 3)}
Write the ordered pairs to be added to R to make the smallest equivalence relation.


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?


R is a relation from {11, 12, 13} to {8, 10, 12} defined by y = x − 3. Then, R−1 is ______________ .


Let A = {1, 2, 3} and B = {(1, 2), (2, 3), (1, 3)} be a relation on A. Then, R is ________________ .


If R is the largest equivalence relation on a set A and S is any relation on A, then _____________ .


In the set Z of all integers, which of the following relation R is not an equivalence relation ?


Mark the correct alternative in the following question:

Let L denote the set of all straight lines in a plane. Let a relation R be defined by lRm if l is perpendicular to m for all l, m  L. Then, R is ______________ .


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


Let L denote the set of all straight lines in a plane. Let a relation R be defined by lRm if and only if l is perpendicular to m ∀ l, m ∈ L. Then R is ______.


Let n be a fixed positive integer. Define a relation R in Z as follows: ∀ a, b ∈ Z, aRb if and only if a – b is divisible by n. Show that R is an equivalance relation


Give an example of a map which is one-one but not onto


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


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


Which of the following is not an equivalence relation on I, the set of integers: x, y


Let A = {1, 2, 3}. Which of the following is not an equivalence relation on A?


Let us define a relation R in R as aRb if a ≥ b. Then R is ____________.


Let A = {1, 2, 3, …. n} and B = {a, b}. Then the number of surjections from A into B is ____________.


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


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 relation R = {(1,1),(2,2),(3,3)} on {1,2,3} 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.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×