Exercise · ZW-LATTICE-OR-ORDER-THEORY-008 · ★★☆ Intermediate
In the poset \(L=\{\hat{0},a,b,c,\hat{1}\}\) with \(\hat{0}<a,b<c<\hat{1}\), what is \(a \wedge b\)?
Choose one option.
Show answer
- D. \(\hat{0}\)
Explanation
The only common lower bound of \(a\) and \(b\) is \(\hat{0}\), so it is their infimum.
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-003 In a lattice, what name is given to the operation x ∨ y?
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- 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-009 Let L be the poset with elements hat0, a, b, c, hat1 and hat0 < a, b < c < hat1 (no relation betwee…
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