Truth tables

Japanese school year: University year 1

What you learn

You will learn to construct truth tables for logical operators such as conjunction, disjunction, negation, and implication to determine the validity of compound propositions. This skill is widely applied in logic circuit design and verifying program branching conditions. Basic knowledge of logical operations and set theory will be beneficial.

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Key points

This equivalence rewrites the conditional statement "if $P$ then $Q$ " as "not $P$ , or $Q$ ". It is false only when premise $P$ is true and conclusion $Q$ is false. Use it to simplify logical reasoning.

(P \implies Q) \iff (\neg P \lor Q)

This formula indicates that statements $P$ and $Q$ have the exact same truth value in every case (logical equivalence). Use it to show that two different formulas mean the same thing.

P \iff Q

This De Morgan's law states that the negation of "both $P$ and $Q$ " is "not $P$ , or not $Q$ ". Use it to simplify negated compound statements in logic and proofs.

\neg(P \land Q) \iff \neg P \lor \neg Q

This formula calculates the total number of truth combinations $N$ for $n$ propositions. Since each proposition has 2 possible states (true or false), $n=3$ requires $2^3 = 8$ rows in a truth table.

N = 2^n

Choose a set to practice.

Practice 1Coming soon