Determine whether the following statement is true or false, and explain your rea-soning:The set {∧, ∨} is functionally complete.

The statement is true. The set {∧, ∨} is functionally complete.

Functional completeness refers to a set of logical operators (in this case, ∧ and ∨) that can be used to construct all possible truth tables by combining them in different ways.

The ∧ operator represents logical conjunction (AND), and the ∨ operator represents logical disjunction (OR).

With these two operators, we can construct the NOT operator, which is necessary for functional completeness. Here's how:

• NOT A can be represented as A ∧ A = A (Identity law)
• NOT A can also be represented as A ∨ A = A (Idempotent law)

Therefore, with ∧, ∨, and the derived NOT, we can construct any possible logical operation, which makes the set {∧, ∨} functionally complete.