## Related questions with answers

A Boolean algebra may also be defined as a partially ordered set with certain additional properties. Let $(B, \leqslant)$ be a partially ordered set. For any $x, y \in B,$ we define the least upper bound of x and y as an element z such that $x \leqslant z, y \leqslant z,$ and if there is any element $Z^{*}$

Solution

VerifiedGiven:

$\begin{align*} x+y&=z\text{ if $z$ is the least upper bound of $x$ and $y$} \\ x\cdot y&=z\text{ if $z$ is the greatest lower bound of $x$ and $y$} \end{align*}$

$z$ is the $\textbf{least upper bound}$ of $x$ and $y$ when:

$\bullet$ $x\preceq z$

$\bullet$ $y\preceq z$

$\bullet$ if there is some element $z^*$ such that $x\preceq z^*$ and $y\preceq z^*$, then $z\preceq z^*$

$z$ is the $\textbf{greatest lower bound}$ of $x$ and $y$ when:

$\bullet$ $z\preceq x$

$\bullet$ $z\preceq y$

$\bullet$ if there is some element $z^*$ such that $z^*\preceq x$ and $z^*\preceq y$, then $z^*\preceq z$

## Create an account to view solutions

## Create an account to view solutions

## Recommended textbook solutions

#### Mathematical Structures for Computer Science

5th Edition•ISBN: 9780716743583Judith L. Gersting#### Mathematical Structures for Computer Science: A Modern Approach to Discrete Mathematics

6th Edition•ISBN: 9780716768647Judith L. Gersting#### Mathematical Structures for Computer Science: Discrete Mathematics and its Applications

7th Edition•ISBN: 9781429215107 (2 more)Judith L. Gersting#### Mathematical Structures for Computer Science

7th Edition•ISBN: 9781464193828Judith L. Gersting## More related questions

- computer science

1/4

- computer science

1/7