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