Discrete math predicate problemIn this problem, we will be using binary predicates F(x, y), G(x,...

kokomocutie88r1

kokomocutie88r1

Answered

2022-07-15

Discrete math predicate problem
In this problem, we will be using binary predicates F(x, y), G(x, y), etc. to represent functions f, g : U U, etc., where U is the universe. Thus, F(x, y) holds iff y = f ( x ), G(x, y) holds iff y = g ( x ), 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 f g.
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 f g.”
- “If f and g are onto functions, then so is f g.”

Answer & Explanation

tykoyz

tykoyz

Expert

2022-07-16Added 17 answers

Explanation:
I'll do the very first one ... see if that helps you get some of the others:
F represents a function:
¬ x y z ( F ( x , y ) F ( x , z ) ¬ y = z )
or, equivalently:
x y z ( ( F ( x , y ) F ( x , z ) ) y = z )
or, equivalently:
x y ( F ( x , y ) ¬ z ( F ( x , z ) ¬ y = z ) )
or, equivalently:
x y ( F ( x , y ) z ( F ( x , z ) y = z ) )

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