Let \(\rho\) be a relation defined on a set of natural numbers N, as \(\rho\)={(x,y)∈N×N:2x+y=4}, then domain A and range B are
- A⊂{x∈N:1≤x≤20} and B⊂{y∈N:1≤y≤39}
- A={x∈N:1≤x≤15} and B={y∈N:2≤y≤30}
- A≡N,B≡Q
- A=Q,B=Q
The Correct Option is A
Solution and Explanation
The correct answer is option (A): A⊂{x∈N:1≤x≤20} and B⊂{y∈N:1≤y≤39}
Top Questions on Relations
- Let \( R \) be a relation on \( \mathbb{Z} \times \mathbb{Z} \) defined by \((a, b) R (c, d)\) if and only if \(ad - bc\) is divisible by 5.
Then \( R \) is: - Let S = {1,2,3,..., 20}, R1 = {(a, b): a divide b}, R2 = {(a, b): a is integral multiple of b} and a, b ∈ S. n(R1 - R2) = ?
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- A = {1, 2, 3, 4} minimum number of elements added to make an equivalence relation on set A containing (1, 3) & (1, 2) in it.
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Concepts Used:
Relations and functions
A relation R from a non-empty set B is a subset of the cartesian product A × B. The subset is derived by describing a relationship between the first element and the second element of the ordered pairs in A × B.
A relation f from a set A to a set B is said to be a function if every element of set A has one and only one image in set B. In other words, no two distinct elements of B have the same pre-image.
Representation of Relation and Function
Relations and functions can be represented in different forms such as arrow representation, algebraic form, set-builder form, graphically, roster form, and tabular form. Define a function f: A = {1, 2, 3} → B = {1, 4, 9} such that f(1) = 1, f(2) = 4, f(3) = 9. Now, represent this function in different forms.
- Set-builder form - {(x, y): f(x) = y2, x ∈ A, y ∈ B}
- Roster form - {(1, 1), (2, 4), (3, 9)}
- Arrow Representation
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