Exercise · ZW-LATTICE-OR-ORDER-THEORY-002 · ★★☆ Intermediate
In the poset of divisors of 12 ordered by divisibility, what is \(4 \wedge (4 \vee 6)\)?
Choose one option.
Show answer
- B. 4
Explanation
First \(4 \vee 6 = 12\), then \(4 \wedge 12 = 4\) since 4 divides 12. This is the absorption law \(x \wedge (x \vee y) = x\).
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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