Propositional wffs and truth tables belong to a system of two-valued logic because everything has one of two values, False or True. Three-valued logic allows a third value of Null or "unknown" (Section 5.3 discusses the implications of three-valued logic on databases). The truth tables for this three-valued system follow.

a. Viewing $N$ as "unknown", explain why it is reasonable to define $T\wedge N=N,F\vee N=N$, and $N^{\prime }=N$.
Suppose the statement, "Flight 237 is on time," is true, the statement, "Runway conditions are icy," is false, and the truth value of the statement, "Flight 51 is on time," is unknown. Find the truth values of the following statements.
b. Runway conditions are not icy and flight 51 is on time.
c. Flight 51 is on time and flight 237 is not.
d. Flight 51 is not on time or runway conditions are not icy.

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