Maths · One-one, into and onto functions
Let and be defined by =a, f(y)= \) =\boldsymbol{c} . \) This function is
Let \( \boldsymbol{A}=\{\boldsymbol{x}, \boldsymbol{y}, \boldsymbol{z}\}, \boldsymbol{B}=\{\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c}\} \) and \( \boldsymbol{f} \) \( A \rightarrow B \) be defined by \( f(x)=a, f(y)= \) \( \boldsymbol{b}, \boldsymbol{f}(\boldsymbol{z})=\boldsymbol{c} . \) This function is
- A. surjective but not injective
- B. injective but not surjective
- C. bijective
- D. none of these
Step-by-step solution
The function f maps each element of A to a distinct element of B, and all elements of B are covered. Hence f is both injective (one-one) and surjective (onto), so it is bijective.
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