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Question
Which of the following functions from A to B are one-one and onto ?
f3 = {(a, x), (b, x), (c, z), (d, z)} ; A = {a, b, c, d,}, B = {x, y, z}.
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Solution
f3 = {(a, x), (b, x), (c, z), (d, z)} ; A = {a, b, c, d,}, B = {x, y, z}
Injectivity:
f3 (a) = x
f3 (b) = x
f3 (c) = z
f3 (d) = z
⇒ a and b have the same image x. (Also c and d have the same image z)
So, f3 is not one-one.
Surjectivity:
Co-domain of f1 ={x, y, z}
Range of f1 =set of images = {x, z}
So, the co-domain is not same as the range.
So, f3 is not onto.
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