Past exam of the year 1 of the computer science course of the University of Oxford / 2023 / Digital systems, linear algebra and introduction to formal proof / 7 / a / Solution

Use $0$ and $1$ for false and true truth values. The truth table is:

The two satisfying rows with $A=B=1$ combine by eliminating $C$, while the remaining satisfying row has $A=B=0,C=1$. An equivalent disjunctive normal form is thereforeExpanding the logical biconditional into its two implications, and using $\neg B\to C\equiv B\vee C$, gives the conjunctive normal formEach form has exactly the same three satisfying assignments as the original propositional formula.