Exercise · ZW-LATTICE-OR-ORDER-THEORY-007 · ★★☆ Intermediate
In the poset of divisors of 60 ordered by divisibility, compute \(10 \vee 15\).
Choose one option.
Show answer
- A. 30
Explanation
The supremum is the least common multiple of 10 and 15 within the divisors of 60, which is 30.
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
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- 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-008 In the poset L=\hat0,a,b,c,hat1\ with hat0<a,b<c<hat1, what is a wedge b?
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