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The sets A and B have same cardinality if and only if there is ___________ from A to B.
- a)One-to-one
- b)One-to-many
- c)Many-to-many
- d)Many-to-one
Correct answer is option 'A'. Can you explain this answer?
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The sets A and B have same cardinality if and only if there is _______...
Explanation:
Cardinality is a measure of the size of a set, which is represented by a cardinal number. Two sets are said to have the same cardinality if there exists a one-to-one correspondence between the elements of the two sets.
- One-to-One Correspondence: A function f from set A to set B is said to be one-to-one if every element of A is mapped to a unique element of B. In other words, no two distinct elements of A are mapped to the same element of B. This is also known as an injective function.
- Many-to-One Correspondence: A function f from set A to set B is said to be many-to-one if there exist at least two distinct elements in A that are mapped to the same element in B. This is also known as a non-injective function.
- One-to-Many Correspondence: A function f from set A to set B is said to be one-to-many if there exists at least one element in B that is not mapped to by any element in A. This is also known as a non-surjective function.
- Many-to-Many Correspondence: A function f from set A to set B is said to be many-to-many if there exist at least two distinct elements in A that are mapped to the same element in B, and there exists at least one element in B that is not mapped to by any element in A.
Therefore, option 'A' is the correct answer as sets A and B have the same cardinality if and only if there exists a one-to-one correspondence between the elements of the two sets.
Cardinality is a measure of the size of a set, which is represented by a cardinal number. Two sets are said to have the same cardinality if there exists a one-to-one correspondence between the elements of the two sets.
- One-to-One Correspondence: A function f from set A to set B is said to be one-to-one if every element of A is mapped to a unique element of B. In other words, no two distinct elements of A are mapped to the same element of B. This is also known as an injective function.
- Many-to-One Correspondence: A function f from set A to set B is said to be many-to-one if there exist at least two distinct elements in A that are mapped to the same element in B. This is also known as a non-injective function.
- One-to-Many Correspondence: A function f from set A to set B is said to be one-to-many if there exists at least one element in B that is not mapped to by any element in A. This is also known as a non-surjective function.
- Many-to-Many Correspondence: A function f from set A to set B is said to be many-to-many if there exist at least two distinct elements in A that are mapped to the same element in B, and there exists at least one element in B that is not mapped to by any element in A.
Therefore, option 'A' is the correct answer as sets A and B have the same cardinality if and only if there exists a one-to-one correspondence between the elements of the two sets.
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The sets A and B have same cardinality if and only if there is _______...
If there is one-to-one correspondence then they have same cardinality.
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