Checking an equivalence with the truth table

To establish whether two formulae are equivalent it is enough to build the respective columns in the truth table and compare them row by row: if they coincide everywhere, the formulae are equivalent.

Example — Checking with the truth table

Let us prove that $p\Rightarrow q\equiv\lnot p\lor q$ by comparing the columns:

p & q & p\Rightarrow q & \lnot p\lor q \\ \hline V & V & V & V \\ V & F & F & F \\ F & V & V & V \\ F & F & V & V \end{array}$$ The two columns coincide in all the rows: hence the two formulae are equivalent.

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Topics: Set theory
Concepts: Logical equivalence · Truth table
Skills: Proving · Reasoning by cases