### How many possible number of reflexive relations are there on a set of 5 elements?

## How many possible number of reflexive relations are there on a set of 5 elements?

Number of reflexive relations

Elements | Any | Equivalence relation |
---|---|---|

3 | 512 | 5 |

4 | 65,536 | 15 |

n | 2n2 | S(n, k) |

OEIS | A002416 | A000110 |

**What is a reflexive relation in sets?**

Reflexive relation on set is a binary element in which every element is related to itself. Consider, for example, a set A = {p, q, r, s}. The relation R1 = {(p, p), (p, r), (q, q), (r, r), (r, s), (s, s)} in A is reflexive, since every element in A is R1-related to itself.

**Which of the following is a reflexive relation if it is defined on the set of integers?**

Q. 1: A relation R is on set A (set of all integers) is defined by “x R y if and only if 2x + 3y is divisible by 5”, for all x, y ∈ A. Hence, R is reflexive.

### How do you prove equivalence relations?

To prove an equivalence relation, you must show reflexivity, symmetry, and transitivity, so using our example above, we can say:

- Reflexivity: Since a – a = 0 and 0 is an integer, this shows that (a, a) is in the relation; thus, proving R is reflexive.
- Symmetry: If a – b is an integer, then b – a is also an integer.

**How many reflexive relations are possible in set A if’n is equals to 4?**

The total number of reflexive relations set with 4 elements = 24.

**How do you know if R is reflexive?**

R is reflexive, i.e. there is a loop at each vertex. R is symmetric, i.e. the arrows joining a pair of different vertices always appear in a pair with opposite arrow directions.

#### How do you prove antisymmetric relations?

To prove an antisymmetric relation, we assume that (a, b) and (b, a) are in the relation, and then show that a = b. To prove that our relation, R, is antisymmetric, we assume that a is divisible by b and that b is divisible by a, and we show that a = b.

**How many reflexive relations are possible in set Aabcd?**

Thus, out of the total 16=222 relations, only 4=2(22−2) are reflexive. Similarly, we can find that for a four-element set, the total number of relations is 242 and out of these 242−4=212 relations are reflexive.

**What is the possible number of reflexive relations on a set of 5 elements?**

What is the possible number of reflexive relations on a set of 5 elements?a)210b)215c)220d)225Correct answer is option ‘C’. Can you explain this answer? | EduRev Computer Science Engineering (CSE) Question Forgot Password? New User? Sign Up I accept the Terms & Conditions . Already Have an Account? Login

## Which is an example of a reflexive relation?

Symmetry, transitivity and reflexivity are the three properties representing equivalence relations. For example, when every real number is equal to itself, the relation “is equal to” is used on the set of real numbers. A reflexive relation is said to have the reflexive property or is meant to possess reflexivity.

**When is a relation neither reflexive nor irreflexive?**

It can be concluded that the relation will be non-reflexive and non-irreflexive if it contains at least one pair of (x, x) and at most (N – 1) pairs of (x, x). Among N pairs of (x, x), the total number of possibilities of choosing any number of pairs except 0 and N – 1 is (2N – 2).

How many possible number of reflexive relations are there on a set of 5 elements? Number of reflexive relations Elements Any Equivalence relation 3 512 5 4 65,536 15 n 2n2 S(n, k) OEIS A002416 A000110 What is a reflexive relation in sets? Reflexive relation on set is a binary element in which every element…