Advertisements
Advertisements
प्रश्न
Let the relation R be defined on the set A = {1, 2, 3, 4, 5} by R = {(a, b) : |a2 – b2| < 8. Then R is given by ______.
Advertisements
उत्तर
Let the relation R be defined on the set A = {1, 2, 3, 4, 5} by R = {(a, b) : |a2 – b2| < 8. Then R is given by {(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 2), (3, 3), (3, 4), (4, 3), (4, 4),( 5, 5)}.
Explanation:
Given, A = {1, 2, 3, 4, 5}
R = {(a, b) : |a2 – b2| < 8}
∴ R = {(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 2), (3, 3), (3, 4), (4, 3), (4, 4),( 5, 5)}
APPEARS IN
संबंधित प्रश्न
If R=[(x, y) : x+2y=8] is a relation on N, write the range of R.
Given an example of a relation. Which is Symmetric but neither reflexive nor transitive.
Show that the relation R defined in the set A of all triangles as R = {(T1, T2) : T1 is similar to T2}, is an equivalence relation. Consider three right angle triangles T1 with sides 3, 4, 5, T2 with sides 5, 12, 13 and T3 with sides 6, 8, and 10. Which triangles among T1, T2 and T3 are related?
Given a non-empty set X, consider P(X), which is the set of all subsets of X. Define the relation R in P(X) as follows:
For subsets A, B in P(X), ARB if and only if A ⊂ B. Is R an equivalence relation on P(X)? Justify your answer.
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 is father of and y}
The following relation is defined on the set of real numbers.
aRb if a – b > 0
Find whether relation is reflexive, symmetric or transitive.
The following relation is defined on the set of real numbers.
aRb if 1 + ab > 0
Find whether relation is reflexive, symmetric or transitive.
Show that the relation '≥' on the set R of all real numbers is reflexive and transitive but not symmetric ?
Given the relation R = {(1, 2), (2, 3)} on the set A = {1, 2, 3}, add a minimum number of ordered pairs so that the enlarged relation is symmeteric, transitive and reflexive.
Let A = {1, 2, 3} and R = {(1, 2), (1, 1), (2, 3)} be a relation on A. What minimum number of ordered pairs may be added to R so that it may become a transitive relation on A.
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 C be the set of all complex numbers and C0 be the set of all no-zero complex numbers. Let a relation R on C0 be defined as
`z_1 R z_2 ⇔ (z_1 -z_2)/(z_1 + z_2)` is real for all z1, z2 ∈ C0.
Show that R is an equivalence relation.
Write the domain of the relation R defined on the set Z of integers as follows:-
(a, b) ∈ R ⇔ a2 + b2 = 25
If R = {(x, y) : x + 2y = 8} is a relation on N by, then write the range of R.
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.
State the reason for the relation R on the set {1, 2, 3} given by R = {(1, 2), (2, 1)} to be transitive ?
Let R be the equivalence relation on the set Z of the integers given by R = { (a, b) : 2 divides a - b }.
Write the equivalence class [0].
A relation ϕ from C to R is defined by x ϕ y ⇔ | x | = y. Which one is correct?
Let R = {(a, a), (b, b), (c, c), (a, b)} be a relation on set A = a, b, c. Then, R is _______________ .
Let A = {1, 2, 3} and B = {(1, 2), (2, 3), (1, 3)} be a relation on A. Then, R is ________________ .
S is a relation over the set R of all real numbers and it is given by (a, b) ∈ S ⇔ ab ≥ 0. Then, S is _______________ .
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 R be a relation on the set N of natural numbers defined by nRm if n divides m. Then, R is _____________ .
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 ______________ .
If A = {a, b, c}, B = (x , y} find A × B.
Let A = {1, 2, 3, 4}, B = {4, 5, 6}, C = {5, 6}. Find A × (B ∪ C).
Let A = {1, 2, 3, 4}, B = {4, 5, 6}, C = {5, 6}. Find (A × B) ∪ (A × C).
Give an example of a map which is neither one-one nor onto
The following defines a relation on N:
x + 4y = 10 x, y ∈ N.
Determine which of the above relations are reflexive, symmetric and transitive.
Total number of equivalence relations defined in the set S = {a, b, c} 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?
Sherlin and Danju are playing Ludo at home during Covid-19. While rolling the dice, Sherlin’s sister Raji observed and noted the possible outcomes of the throw every time belongs to set {1,2,3,4,5,6}. Let A be the set of players while B be the set of all possible outcomes.
A = {S, D}, B = {1,2,3,4,5,6}
- Let R ∶ B → B be defined by R = {(x, y): y is divisible by x} is ____________.
Sherlin and Danju are playing Ludo at home during Covid-19. While rolling the dice, Sherlin’s sister Raji observed and noted the possible outcomes of the throw every time belongs to set {1,2,3,4,5,6}. Let A be the set of players while B be the set of all possible outcomes.
A = {S, D}, B = {1,2,3,4,5,6}
- Raji wants to know the number of relations possible from A to B. How many numbers of relations are possible?
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 ____________.
If A = {1,2,3}, B = {4,6,9} and R is a relation from A to B defined by ‘x is smaller than y’. The range of R 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 ______.
