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