Part IV (20 pt.) Indicate the properties of each of the following functions and

Question

Part IV (20 pt.) Indicate the properties of each of the following functions and relations. For each function, indicate whether it is injective (one-to-one), surjective (onto), and/or bijective. For each relation, indicate whether it is reflexive, anti-reflexive, symmetric, anti-symmetric, and/or transitive. 1. (5 pt.) f is a function from Z to Z such that f(x) Ix +1]. 2. (5 pt.) g is a function from Z to Z such that g(x) lx/2]. 3. (10 pt.) Let A be a finite non-empty set. S is a relation on the power set of A such that (X, Y) E s if and only if IX/>, where IX1 is the cardinality of X

Explanation / Answer

1) We can consider |X+1| as x=+-1 but the function f:z->z such that f(x)=|X+1| is a surjective function as it can accept the negative values also, each output value is gonna be a valid output as it points and equals to co-domain, so it is surjective function.

2) G:z->z such that g(x)=[x/2] is a bijective function as it's range accepts negative and positive integers and each element in setA maps to one of the particular element in setB so it satisfies one on one and onto function.

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---