Discrete Structures208110 marksNumerical: function properties, floor/ceilingInjective and Bijective Functions
Determine whether the function f(x) = x-1 from set of integers to the set of integers is injective, surjective or bijective. Write the type of Fuzzy set operations with their definition. Give the floor and ceiling value of 1.2 and -1.2.
Determine whether the function f(x) = x-1 from set of integers to the set of integers is injective, surjective or bijective. Write the type of Fuzzy set operations with their definition. Give the floor and ceiling value of 1.2 and -1.2.[10]
- Function: $f(x) = x - 1$, with $f: \mathbb{Z} \to \mathbb{Z}$ (integers to integers) - Task 2: Types of fuzzy set operations with definitions - Values for floor/ceiling: $1.2$ and $-1.2$ All data present. Proceeding to solve. --- Assume $f(x1) = f(x2)$: $$x1 - 1 = x2 - 1 \implies x1 = x2$$ Sinc...