Exercise · ZW-LATTICE-OR-ORDER-THEORY-001 · ★☆☆ Basic
What is the supremum of 4 and 6 in the poset of divisors of 12 ordered by divisibility?
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- C. 12
Explanation
The supremum is the least common upper bound; 12 is a multiple of both 4 and 6 and is the smallest such divisor of 12.
Review the concept: Lattice or order theory
A lattice is a partially ordered set (L, ≤) in which every pair of elements x and y has a supremum (x ∨ y) and an infimum (x ∧ y).
\[x \vee y = \sup\{x,y\}, \quad x \wedge y = \inf\{x,y\}\]
More practice problems: lattice or order theory
- ZW-LATTICE-OR-ORDER-THEORY-002 In the poset of divisors of 12 ordered by divisibility, what is 4 wedge (4 vee 6)?
- ZW-LATTICE-OR-ORDER-THEORY-003 In a lattice, what name is given to the operation x ∨ y?
- ZW-LATTICE-OR-ORDER-THEORY-004 In the poset of subsets of \1,2,3\ ordered by inclusion, what is \1,2\ vee \2,3\?
- ZW-LATTICE-OR-ORDER-THEORY-005 What is the supremum of 2 and 3 in the poset of divisors of 6 ordered by divisibility?
- ZW-LATTICE-OR-ORDER-THEORY-006 In the poset of divisors of 30 ordered by divisibility, compute 6 wedge 10.
- ZW-LATTICE-OR-ORDER-THEORY-007 In the poset of divisors of 60 ordered by divisibility, compute 10 vee 15.
- ZW-LATTICE-OR-ORDER-THEORY-008 In the poset L=\hat0,a,b,c,hat1\ with hat0<a,b<c<hat1, what is a wedge b?
- ZW-LATTICE-OR-ORDER-THEORY-009 Let L be the poset with elements hat0, a, b, c, hat1 and hat0 < a, b < c < hat1 (no relation betwee…