A. Reflexive
B. Antisymmetric
C. Symmetric
Let A = {a, b, c, d, e, f, g} and R = {(a, a), (b, b), (c, d), (c, g), (d, g), (e, e), (f, f), (g, g)} be a relation of A. Which of the following property (properties) is (are) satisfied by the relation R?
Correct Answer: (d) B and Not A
Solution:If a binary relation R over a set X relates every element of x to itself. It is said to be reflexive since (c. e) and (a, d) is not given in the given question it is not reflexive.
• A binary relation is anti symmetric is there is no pair of distinct elements of X each of which is related by R to the other. The given relation R is anti symmetric because for (c, d), (d, c) is not present in R. Similarly for (c, g) and (d, g).
A binary relation is a type of binary relation An example is the relation is equal to because it a = b is true then b = a is also true.
Here since (c, d) is pair in a given relations R for which (d, c) is not present in it. So it violates the symmetric property of the relation, Hence it is not symmetric.