How many relations can be defined on a set with 4 elements?

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How many relations can be defined on a set with 4 elements?

Now, any subset of AXA will be a relation, as we know that with n elements, 2^n subsets are possible, So in this case, there are 2^4=16 total possible relations.

How many elements will AxB have?

Total number of elements in A×B = 2 × 4 = 8.

How many subsets will AxB have?

So, number of subsets of A X B will be 2^6 i.e. 64.

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What is AxB in set theory?

Cartesian Product of Two Sets | Cross Product of Sets Let us consider A and B to be two non-empty sets and the Cartesian Product is given by AxB set of all ordered pairs (a, b) where a ∈ A and b ∈ B. AxB = {(a,b) | a ∈ A and b ∈ B}. If A = B then AxB is called the Cartesian Square of Set A and is represented as A2.

How many relations are possible in a set A having 3 elements?

Answer: A relation is just a subset of A×A, and so there are 2n2 relations on A. So a 3-element set has 29 = 512 possible relations.

How many relations can be defined on a set A if number of elements in A is N?

If a set A has n elements then number of relations on A is given by 2n2.

How many relations are possible from a set A of N elements to another set B of N elements?

How many relations can A to B have?

Hence, the number of relations from A to B is 16. Note: To solve such problems of sets we need to use the formula of the number of relations from one set to another can be written as 2(number of elements in first set) × (number of elements in second set).

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What is the value of 4?

Here the digit 4 is in the tens column. Hence, the value of the digit 4 will be i.e. 40 or forty.

How many relations are possible in set A such that n a 2?

How many relations are there on AXB?

(If A and B are the same, then a relation on AxA is also called a relation on A.). 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.

How many (NxM) relations can be defined from a to B?

A subset of the Cartesian product (AxB)of two sets A, B is a relation 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 .

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How many relations are there between A and B?

A relation between A and B is a subset of the Cartesian product A × B. As A × B has 4 × 3 = 12 elements, it has 2 12 = 4096 subsets. So that is the number of relations.

How many subsets of (a x b ) have 3×4 elements?

If A has 3 elements and B has 4 elements then (A x B ) has (3 x 4 ) = 12 elements in it . Therefore no. of subsets of (A x B) = 2^ (12) = 4096 ; that are the required numbers of relations from A to B.