2.6.2. Part (b): Composition of Functions

Try these first

1. 1.

   What is a surjective function? Give an example.

   Hint

   Think about functions that cover all outputs.

2. 2.

   How does an injective function differ from a surjective function?

   Hint

   Consider how functions can map inputs to outputs.

3. 3.

   What is true about a surjective function?

   • All elements in the domain are mapped to unique elements.
   • Every element in the codomain is covered.
   • It cannot have repeated outputs.

   Hint

   Focus on what it means when every output has a backing input.

4. 4.

   A function can be surjective in finite sets. True or False?

   Hint

   Recall the definition of surjectivity in context.

5. 5.

   Imagine a function f: {1, 2, 3, 4} → {a, b, c} is defined. What can you conclude about its surjectivity and injectivity?

   Hint

   Reflect on the cardinality principle in set functions.

6. 6.

   Define a surjective function from the set of all integers to a set containing two elements. Provide justification for your answer.

   Hint

   Consider how to classify integers into distinct categories.