Transformation (function) - Quiz
- 1. What is another term for a transformation?
A) Subset
B) Vector
C) Self-map
D) Cardinality
- 2. A transformation usually has what kind of underpinning?
A) Statistical
B) Algebraic
C) Geometrical
D) Numerical
- 3. How is a standard transformation generally denoted regarding its domain and codomain sets X?
A) f: X → X
B) f: A → B
C) X: f → f
D) f: X → Y
- 4. Which of the following is an example of a linear transformation?
A) Partial functions
B) Transformations of vector spaces
C) Cardinality numbers
D) Regular semigroups
- 5. Which of the following is considered a specific affine transformation?
A) Projection
B) Composition
C) General mapping
D) Rotation
- 6. Which transformation type is explicitly mentioned alongside rotations and translations?
A) Limits
B) Integrals
C) Derivatives
D) Reflections
- 7. In the alternative terminological convention, the term 'transformation' is reserved exclusively for what?
A) Bijections
B) Surjections
C) Partial functions
D) Injections
- 8. What is a partial transformation defined as?
A) A function f: X → X
B) A linear transformation of vector spaces
C) A bijection from X to itself
D) A function f: A → B where A and B are subsets of X
- 9. What mathematical structure is formed by the set of all transformations on a given base set together with function composition?
A) Subset group
B) Vector space
C) Regular semigroup
D) Finite field
- 10. How many total transformations are there for a finite set of cardinality n?
A) 2n
B) (n+1)n
C) nn
D) n!
- 11. How many partial transformations are there for a finite set of cardinality n?
A) n!
B) 2n
C) (n+1)n
D) nn
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