Solution to Let X= {1, 2, 3, 4}Y= {a, b, c} and Z={1,2} 1. Define K: Y→X … - Sikademy
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Archangel Macsika

Let X= {1, 2, 3, 4}Y= {a, b, c} and Z={1,2} 1. Define K: Y→X as follows: K(a) = 1, K(b) = 2, K(c) = 3, and K(c) = 4. Is K onto? If not explain. 2. Using arrow diagram, find one function from X to Y that is Onto but not One-to-One 3. Define a function G: Y→Z that is onto and one-to-one and represent through matrix.

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1) Given defined K is onto since every element of co-domain is in range of K. But defined K is not a function because one element has 2 images.

2) 1\to a, 2 \to b, 3 \to c, 4 \to c . This is function and not one-one since 3 and 4 has same image. This is onto also.

3) Function is not defined where function is one-one because co-domain has less element than domain. Hence, atleast two element have one image which can-not be one-one.

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