Let F be the set of all functions from {1,...,n} to {0,1}. Define the binary relation ≼ on F as follows:

∀f,g ∈ F, f ≼ g if and only if ∀x ∈ {1,...,n}, f(x) ≤ g(x), where 0 ≤ 1.

Which of the following statement(s) is/are TRUE?

Question

Let F be the set of all functions from {1,...,n} to {0,1}. Define the binary relation ≼ on F as follows:

∀f,g ∈ F, f ≼ g if and only if ∀x ∈ {1,...,n}, f(x) ≤ g(x), where 0 ≤ 1.

Which of the following statement(s) is/are TRUE?

Accepted Answer

(F, ≼) is a lattice. (F, ≼) is a lattice because it satisfies the properties of a partially ordered set where every pair of elements has both a least upper bound (join) and a greatest lower bound (meet), which can be defined in terms of the pointwise maximum and minimum of the functions.

Let F be the set of all functions from {1,...,n} to {0,1}. Define the binary relation ≼ on F as follows: ∀f,g ∈ F, f ≼ g if and only if ∀x ∈ {1,...,n}, f(x) ≤ g(x), where 0 ≤ 1. Which of the following statement(s) is/are TRUE?

Solution

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