Schaum's Outline of Discrete Mathematics, Third Edition (Schaum's Outlines)

CHAP. 14] ORDERED SETS AND LATTICES 367

14.74. Geometrically, an elementa=Iis meet-irreducible

if and only ifahas only one immediate successor.

(a)a,c,d,e,I; (b)a,b,d,f,g,I; (c) 4, 6, 12,

15, 60.

14.75. (a) Ifa≤cthena∨c=c. Hencea∨(b∧c)=

(a∨b)∧(a∨c)=(a∨b)∧c; (b) Herea≤c. But

a∨(b∧c)=a∨ 0 =aand(a∨b)∧c=I∧c=c;

hencea∨(b∧c)=(a∨b)∧c.