Which of the following relations between two sets are functions?
Which of the following relations between two sets are functions?
In the image given below, the second element in the first set has no image in the second set. Therefore, this relation is not a function.
In the image given below, all the elements in the first set have images, and each element has one and only one image. Therefore, this relation is a function.
In the image given below, the second element of the first set is mapped to two different elements or in other words, it has two images. Therefore, this relation is not a function.
In the image given below, all the elements in the first set have only one image. Therefore, this relation is a function.
Note: In a function, the elements of the first set can have common images but a single element is not allowed to have multiple images.
In the image given below, the second element in the first set has no image in the second set. Therefore, this relation is not a function.
In the image given below, all the elements in the first set have images, and each element has one and only one image. Therefore, this relation is a function.
In the image given below, the second element of the first set is mapped to two different elements or in other words, it has two images. Therefore, this relation is not a function.
In the image given below, all the elements in the first set have only one image. Therefore, this relation is a function.
Note: In a function, the elements of the first set can have common images but a single element is not allowed to have multiple images.
