Consider the ordering relation a | b ⊆ N x N over natural numbers N such that a | b if there exists c belong to N such that a*c=b. Then ___________
A. | is an equivalence relation
B. It is a total order
C. Every subset of N has an upper bound under |
D. (N,|) is a lattice but not a complete lattice
Answer:D
Consider the ordering relation a | b ⊆ N x N over natural numbers N such that a | b if there exists c belong to N such that a*c=b. Then ___________
A. | is an equivalence relation B. It is a total order C. Every subset of N has an upper bound under | D. (N,|) is a lattice but not a complete lattice
Explanation: A set is called lattice if every finite subset has a least upper bound and greatest lower bound. It is termed as a complete lattice if every subset has a least upper bound and greatest lower bound. As every subset of this will not have LUB and GLB so (N,|) is a lattice but not a complete lattice.