Truth Table Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
Build a truth table to verify that p⇒qp \Rightarrow q is logically equivalent to ¬p∨q\neg p \lor q.

Solution

  1. 1
    List all rows: (T,T),(T,F),(F,T),(F,F)(T,T), (T,F), (F,T), (F,F).
  2. 2
    Compute p⇒qp \Rightarrow q: T,F,T,TT, F, T, T.
  3. 3
    Compute ¬p\neg p: F,F,T,TF, F, T, T. Then ¬p∨q\neg p \lor q: T,F,T,TT, F, T, T.
  4. 4
    The columns for p⇒qp \Rightarrow q and ¬p∨q\neg p \lor q match in every row, confirming equivalence.

Answer

p⇒q≡¬p∨qp \Rightarrow q \equiv \neg p \lor q
Two logical expressions are equivalent if they have identical truth values in every row of their truth tables. This equivalence is fundamental in propositional logic.

About Truth Table

A table that systematically lists every possible combination of truth values for the input variables and the resulting truth value of the expression.

Learn more about Truth Table →

More Truth Table Examples

Example 1 easy

Construct the truth table for [formula].

Example 3 medium

Construct the truth table for [formula] and verify it equals [formula] (De Morgan's Law).

Example 4 medium

Construct the truth table for [formula].

← All Truth Table Examples Truth Table Concept

Related Concepts

Logical Statement