Discrete math predicate problemIn this problem, we will be using binary predicates F(x, y), G(x,...
Discrete math predicate problem
In this problem, we will be using binary predicates F(x, y), G(x, y), etc. to represent functions f, , etc., where U is the universe. Thus, F(x, y) holds iff , G(x, y) holds iff , etc.
1. Write predicate statements that expresses the following facts:
- F represents a function.
- F represents a one-to-one function.
- F represents an onto function.
- F and G represent inverse functions of one another.
- H represents the composition function .
2. Use binary predicates representing functions to give formal proofs (in the style of Sec 1.6 of the following statements:
- “If f and g are one-to-one functions, then so is .”
- “If f and g are onto functions, then so is .”