Advertisements
Advertisements
प्रश्न
Let X = {a, b, c, d} and R = {(a, a), (b, b), (a, c)}. Write down the minimum number of ordered pairs to be included to R to make it transitive
Advertisements
उत्तर
Given X = {a, b, c, d}
R = {(a, a), (b, b), (a, c)}
R is transitive.
We need not add any pair.
APPEARS IN
संबंधित प्रश्न
Let R be the relation on Z defined by R = {(a, b): a, b ∈ Z, a – b is an integer}. Find the domain and range of R.
Let R be a relation on N × N defined by
(a, b) R (c, d) ⇔ a + d = b + c for all (a, b), (c, d) ∈ N × N
Show that:
(i) (a, b) R (a, b) for all (a, b) ∈ N × N
If R is a relation defined on the set Z of integers by the rule (x, y) ∈ R ⇔ x2 + y2 = 9, then write domain of R.
If R = [(x, y) : x, y ∈ W, 2x + y = 8], then write the domain and range of R.
Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1), (y, 2), (z, 1) are in A × B, write A and B
A relation ϕ from C to R is defined by x ϕ y ⇔ |x| = y. Which one is correct?
If A = {a, b, c}, B = {x, y}, find A × B, B × A, A × A, B × B
Let A = {6, 8} and B = {1, 3, 5}
Show that R1 = {(a, b)/a ∈ A, b ∈ B, a − b is an even number} is a null relation. R2 = {(a, b)/a ∈ A, b ∈ B, a + b is odd number} is an universal relation
Select the correct answer from given alternative.
Let R be a relation on the set N be defined by {(x, y)/x, y ∈ N, 2x + y = 41} Then R is ______.
Find the domain of the function f(x) = `sqrt(1 + sqrt(1 - sqrt(1 - x^2)`
On the set of natural numbers let R be the relation defined by aRb if 2a + 3b = 30. Write down the relation by listing all the pairs. Check whether it is symmetric
In the set Z of integers, define mRn if m − n is divisible by 7. Prove that R is an equivalence relation
Which statement defines a relation from set \(A\) to set \(B\)?
In the ordered pair \((a,b)\), what are \(a\) and \(b\), respectively?
For a relation \(R\), the range is the set of all:
The Cartesian product \(A\times A\) has \(9\) elements and contains \((-1,0)\) and \((0,1)\). What is \(A\)?
For \(A=\{-1,0,1\}\), which ordered pair is a remaining element of \(A\times A\) besides \((-1,0)\) and \((0,1)\)?
Let \(A=\{1,2,3,4,5\}\), \(B=\{1,4,5\}\), and \((x,y)\in R\) imply \(x
For \(R=\{(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)\}\), what is the domain?
Let \(A=\{1,2,3\}\), \(B=\{3,4\}\), and \(C=\{4,5,6\}\). What is \(A\times(B\cap C)\)?
