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Question

# Use a truth table to verify the distributive law p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r).

Solution

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DEFINITIONS

Two propositions are equivalent, if they have the same truth value for every possible combination of truth values for the variables ($p,q,r,...$).

TRUTH TABLE

A conjunction $p\wedge q$ is true, if both (sub)propositions ($p$ and $q$) are true.

A disjunction $p\vee q$ is true, if either of the (sub)propositions ($p$ or $q$) are true.

A negation $\neg p$ is true, if the (sub)proposition $p$ is false.

A conditional statement $p\rightarrow q$ is true, if $p$ is false, or if both (sub)propositions are true.

A biconditional statement $p\leftrightarrow q$ is true, if both (sub)propositions are true or if both (sub)propositions are false.

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