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GO Classes DPP | GATE CS | Discrete Mathematics| Set Theory

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A function $f$ is ______ , if and only if, each element in the co-domain of $f$ is the image of atmost one element in the domain. Fill the blank space:

  1. Neither one-one nor onto
  2. Both one-one and onto
  3. One-one
  4. Onto

3 Answers

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  • The definition of an Injective (one-one) function is: $f(x_1) = f(x_2) \implies x_1 = x_2$.

  • In terms of mapping: No two distinct elements in the domain can map to the same element in the co-domain.

  • This implies each $y$ in the co-domain can have either 0 or 1 pre-image.

  • "At most one" perfectly describes this condition.

option C is correct. 

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