Determine whether the Relation R in the set A=1,2,3,4,5,6 as R={(x,y):yisdivisiblebyx}  is reflexive, symmetric and transitiveHard

To determine whether the relation R is reflexive, symmetric, and transitive, we need to check the properties of each.

1. Reflexive: A relation R in a set A is reflexive if every element is related to itself. In other words, for every a in A, (a, a) must be in R. In this case, every number in the set A is divisible by itself. Therefore, the relation R is reflexive.

2. Symmetric: A relation R in a set A is symmetric if for every (a, b) in R, (b, a) is also in R. In this case, if y is divisible by x, it does not necessarily mean that x is divisible by y. For example, (2, 4) is in R because 4 is divisible by 2, but (4, 2) is not in R because 2 is not divisible by 4. Therefore, the relation R is not symmetric.

3. Transitive: A relation R in a set A is transitive if for every (a, b) in R and (b, c) in R, (a, c) is also in R. In this case, if y is divisible by x and z is divisible by y, then z is also divisible by x. For example, if (2, 4) is in R and (4, 8) is in R, then (2, 8) is also in R because 8 is divisible by 2. Therefore, the relation R is transitive.

In conclusion, the relation R is reflexive and transitive, but not symmetric.