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If R is a relation from a non – empty set A to a non – empty set B, then
- a)R⊂A×B.
- b)R=A∪B
- c)R=A∩B
- d)R=A×B
Correct answer is option 'A'. Can you explain this answer?
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If R is a relation from a non – empty set A to a non – emp...
Let A and B be two sets. Then a relation R from set A to set B is a subset of A × B. Thus, R is a relation from A to B ⇔ R ⊆ A × B.
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If R is a relation from a non – empty set A to a non – emp...
-empty set A to a non-empty set B, then R is a subset of A x B, where A x B is the Cartesian product of A and B.
The Cartesian product A x B is defined as the set of all ordered pairs (a, b), where a is an element of A and b is an element of B. In other words, A x B = {(a, b) | a ∈ A and b ∈ B}.
A relation R from A to B is a subset of A x B, meaning that every element of R is an ordered pair (a, b) where a ∈ A and b ∈ B. Intuitively, a relation is a set of pairs of objects, where the first object in each pair comes from A and the second object comes from B.
For example, if A = {1, 2, 3} and B = {a, b, c}, then A x B = {(1, a), (1, b), (1, c), (2, a), (2, b), (2, c), (3, a), (3, b), (3, c)}. If R is the relation {(1, b), (2, a), (3, c)}, then R is a subset of A x B.
Note that not every subset of A x B is a relation from A to B. A relation must satisfy certain properties, depending on the context in which it is defined. For example, a function is a special kind of relation that has the property that each element in A is associated with exactly one element in B.
The Cartesian product A x B is defined as the set of all ordered pairs (a, b), where a is an element of A and b is an element of B. In other words, A x B = {(a, b) | a ∈ A and b ∈ B}.
A relation R from A to B is a subset of A x B, meaning that every element of R is an ordered pair (a, b) where a ∈ A and b ∈ B. Intuitively, a relation is a set of pairs of objects, where the first object in each pair comes from A and the second object comes from B.
For example, if A = {1, 2, 3} and B = {a, b, c}, then A x B = {(1, a), (1, b), (1, c), (2, a), (2, b), (2, c), (3, a), (3, b), (3, c)}. If R is the relation {(1, b), (2, a), (3, c)}, then R is a subset of A x B.
Note that not every subset of A x B is a relation from A to B. A relation must satisfy certain properties, depending on the context in which it is defined. For example, a function is a special kind of relation that has the property that each element in A is associated with exactly one element in B.
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If R is a relation from a non – empty set A to a non – empty set B, thena)R⊂A×B.b)R=A∪Bc)R=A∩Bd)R=A×BCorrect answer is option 'A'. Can you explain this answer?
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If R is a relation from a non – empty set A to a non – empty set B, thena)R⊂A×B.b)R=A∪Bc)R=A∩Bd)R=A×BCorrect answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If R is a relation from a non – empty set A to a non – empty set B, thena)R⊂A×B.b)R=A∪Bc)R=A∩Bd)R=A×BCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If R is a relation from a non – empty set A to a non – empty set B, thena)R⊂A×B.b)R=A∪Bc)R=A∩Bd)R=A×BCorrect answer is option 'A'. Can you explain this answer?.
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