In Theorem 12.3, we showed that [ and \ satisfy the distributive properties: A [ .B \ C / D .A [ B/ \ .A [ C / and A \ .B [ C / D .A \ B/ [ .A \ C /:These equations can be rewritten with ^ in place of \ and _ in place of [:a _ .b ^ c/ D .a _ b/ ^ .a _ c/ anda ^ .b _ c/ D .a ^ b/ _ .a ^ c/: Give an example of a lattice for which the distributive laws are false

L27 - 2 We introduce a new method that applies to many limits of this form: L’Hˆ opital’s Rule ▯ Suppose that f and g are diﬀerentiable and g (x) ▯=0er a (except possibly at a). Suppose that lim f(x)=0a ndl g(x)=0 x→a x→a or x→a f(x)= ±∞ and...