injective

$g(.)$ is a function from A to B, $f(.)$ is a function from B to C, and their composition defined as $f(g(.))$ is a mapping from A to C. If $f(.)$ and $f(g(.))$ are onto (surjectiv...

Let $$f:A \to B$$ be an onto (or surjective) function, where A and B are nonempty sets. Define an equivalence relation $$\sim$$ on the set A as $${a_1} \sim {a_2}$$ if $$f({a_1}) =...

Let $$X$$ and $$Y$$ denote the sets containing $$2$$ and $$20$$ distinct objects respectively and $$𝐹$$ denote the set of all possible functions defined from $$X$$ to $$Y$$. Let $...

Consider the following two statements: i. A hash function (these are often used for computing digital signatures) is an injective function. ii. encryption technique such as DES per...