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Let A = {–1, 0, 1, 2} and B = {2, 3, 4, 5}. Find which of the following are function from A to B. Give reason.
(i) f = {(–1, 2), (-1, 3), (0, 4), 1,5)}
(ii) g = {(0, 2), (1, 3), (2, 4)}
(iii) h = {(-1, 2), (0, 3), (1, 4), (2, 5)}
(i) Given: A = {-1, 0, 1, 2} and B = {2, 3, 4, 5}
Function:
(i) all elements of the first set are associated with the elements of the second set.
(ii) An element of the first set has a unique image in the second set.
f = {(–1, 2), (-1, 3), (0, 4), (1, 5)}
Here, -1 is coming twice.
Hence, it does not have a unique (one) image.
∴ f is not a function
(ii) Given: A = {-1, 0, 1, 2} and B = {2, 3, 4, 5}
Function:
(i) all elements of first set is associated with the elements of second set.
(ii) An element of first set has a unique image in second set.
g = {(0, 2), (1, 3), (2, 4)}
Here, -1 is not associated with any element of set B
Hence, it does not satisfy the condition of the function
∴ g is not a function.
(iii) Given: A = {-1, 0, 1, 2} and B = {2, 3, 4, 5}
Function:
(i) all elements of first set is associated with the elements of second set.
(ii) An element of first set has a unique image in second set.
h = {(-1, 2), (0, 3), (1, 4), (2, 5)}
Here, (i) all elements of set A are associated to element in set B.
(ii) an element of set A is associated to a unique element in set B.
∴ h is a function.