Advertisements
Advertisements
Question
Represent the given relation by
(a) an arrow diagram
(b) a graph and
(c) a set in roster form, wherever possible
{(x, y) | x = 2y, x ∈ {2, 3, 4, 5}, y ∈ {1, 2, 3, 4}
Advertisements
Solution
x = {2, 3, 4, 5} y = {1, 2, 3, 4}
x = 2y
2y = x
y = `x/2`
If `x = 2 ⇒ y = x/2 = 2/2 = 1`
if `x = 3 ⇒ y = x/2 = 3/2`
If `x = 4 ⇒ y = x/2 = 4/2 = 2`
If `x = 5 ⇒ y = x/2 = 5/2`
(a) Arrow diagram
(b) Graph
(c) Roster form R = {(2, 1) (4, 2)}
APPEARS IN
RELATED QUESTIONS
Determine the domain and range of the relation R defined by
(ii) R = {(x, x3) : x is a prime number less than 10}
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:
(ii) (a, b) R (c, d) ⇒ (c, d) R (a, b) for all (a, b), (c, d) ∈ N × N
Write the relation in the Roster Form. State its domain and range
R7 = {(a, b)/a, b ∈ N, a + b = 6}
Select the correct answer from given alternative.
The relation ">" in the set of N (Natural number) is
Answer the following:
Show that the relation R in the set A = {1, 2, 3, 4, 5} Given by R = {(a, b)/|a − b| is even} is an equivalence relation.
Let A = {a, b, c}. What is the equivalence relation of smallest cardinality on A? What is the equivalence relation of largest cardinality on A?
Choose the correct alternative:
Let f : R → R be defined by f(x) = 1 − |x|. Then the range of f is
Which condition must hold for a relation to be a function from \(A\) to \(B\)?
For \(A=\{-1,0,1\}\), which ordered pair is a remaining element of \(A\times A\) besides \((-1,0)\) and \((0,1)\)?
Given \(A=\{1,2,3,4,5\}\), which relation consists of ordered pairs satisfying \(x+y=5\), where \(x,y\in A\)?
