91Ó°ÊÓ

Determine whether the indicated set with the indicated relation is a lattice. The set of all positive divisors of 70 with \(a \leq b\) to mean \(a\) divides \(b\).

Let \(R\) be a Boolean ring with unity 1 and for \(a, b \in R\) define $$ \begin{array}{c} a \vee b=a+b-a b \\ a \wedge b=a b \end{array} $$ Show that \(R\) with \(v\) and \(\wedge\) is a Boolean algebra with unity \(1,\) zero element \(0,\) and \(a^{\prime}=1-a\)