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How many relations are there from a set A with M elements to a set B with n elements?
Answer: If there are n elements in the set A and m elements in the set B, then there will be (nxm) elements in AxB . Accordingly, there will be 2^(nxm) subsets of AxB and therefore there can be defined 2^(nxm) relations from A to B .
How many distinct functions can be defined from set A to set B?
There are 9 different ways, all beginning with both 1 and 2, that result in some different combination of mappings over to B. The number of functions from A to B is |B|^|A|, or 32 = 9. Let’s say for concreteness that A is the set {p,q,r,s,t,u}, and B is a set with 8 elements distinct from those of A.
How many relation can AxB have if set A has four elements and set B has three elements?
If A has four elements and B has three elements, then AxB has 4*3=12 elements. So the question becomes, How many subsets are there of a 12-element set? The number of subsets of an n element set is 2^n, so the number of relations on AxB is 2^12=4096.
What is the total number of functions defined from A to B if’n A 2 and N B 3?
Hence , the answer is 64.
What is distinct relation?
It is Related to the definition of a particular tuple. Named relation defined by a set of attribute and domain name pairs. Relation name is distinct from all other relation names in relational schema. Each cell of relation contains exactly one atomic (single) value. Each attribute has a distinct name.
How many relations can be defined from A and B?
The number of relations that can be defined from A and B is: Here, O(A)=m and O(B)=n. Was this answer helpful? Let Z be the set of integers and R be the relation defined in Z such that aRb if a−b is divisible by 3.
How do you find 2^(NxM) relations from a to B?
If there are n elements in the set A and m elements in the set B, then there will be (nxm) elements in AxB . Accordingly, there will be 2^ (nxm) subsets of AxB and therefore there can be defined 2^ (nxm) relations from A to B . If A & B are two sets having 3 elements in common.
How many subsets of (a x b) = 2^(Mn)?
Here given A, B are two sets containing respectively m & n elements therefore no. of elements in (A x B) = m n, consequently no. of subsets of (A x B) = 2^ (m.n) = no. of relations from A to B (including the empty relation and the complete relation).
How many N^m functions are there from a to B?
If A and B are finite sets with m and n elements, then there are exactly n^m functions from A to B. This is because each of the m elements can be mapped in n ways independently of each other. Hence there are n×n×…..n (m times product) = n^m such functions. Let A, B both be finite set, containing respectively m & n elements.