Relation and function
Formula sheet
Class: 12
# functions:
o The total number of functions from a set A to a set B:
Total number of functions = ∣B∣∣A∣
Where:
∣A∣ is the number of elements in set A (domain).
∣B∣ is the number of elements in set B (codomain).
o The total number of onto functions (also called surjective
functions) from a set A to a set B:
Total onto functions=∣B∣∣A∣−functions that are not onto
Total onto functions =
Key Conditions
If m<n < (i.e., fewer elements in the domain than in the
codomain), no onto Fn is possible as at least one element of B
will not have a preimage.
So, if m<n , the total onto functions = 0.
Formula sheet
Class: 12
# functions:
o The total number of functions from a set A to a set B:
Total number of functions = ∣B∣∣A∣
Where:
∣A∣ is the number of elements in set A (domain).
∣B∣ is the number of elements in set B (codomain).
o The total number of onto functions (also called surjective
functions) from a set A to a set B:
Total onto functions=∣B∣∣A∣−functions that are not onto
Total onto functions =
Key Conditions
If m<n < (i.e., fewer elements in the domain than in the
codomain), no onto Fn is possible as at least one element of B
will not have a preimage.
So, if m<n , the total onto functions = 0.
