Question

Over the Boolean algebra {B}^2, element x is related to element

y iff x. y=x. is a partial order

Answer 1

In Boolean algebra, the relation between elements x and y can be represented by the expression x.y=x, which is a partial order.

Step-by-step explanation:

In Boolean algebra, the relation between elements x and y can be represented by the expression x.y=x. A partial order is a relation that is reflexive, antisymmetric, and transitive. Here, the relation x.y=x satisfies these properties and therefore forms a partial order.

For example, let's consider the elements x=1 and y=0. When we substitute these values into the expression x.y=x, we get 1.0=1, which is true. Similarly, when we substitute y=1 and x=0, we get 0.1=0, which is also true. This shows that the relation x.y=x holds in both directions, making it a partial order.