Difference Between Biconditional & Conditional

Plain English Equivalents

• Statements in logic are often precise versions of ordinary speech; the conditional is the rough equivalent of "implies;" the logic statement A ' B means given that A is true, it is logical that B is also true. The biconditional is the rough equivalent of "equals".

Truth Tables for Conditionals and Biconditionals

• The truth or falsity of logical statements is often represented in what are known as truth tables. In a truth table there is a column for each atomic statement (represented by letters: A, B, and so on) of the overall logic statement, listing every combination of their truth and falsity as well as the truth of the compound statements:

  If A is true and B is true, both the conditional and biconditional are true

  If A is true and B is false, both the conditional and biconditional are false

  If A is false and B is true, the conditional is true and the biconditional is false

  If A is false and B is false, the conditional and the biconditional are true.

Implications of the Conditional and Biconditional

• In logic, you can deduce several general abstract relationships about conditionals and biconditionals. If the biconditional is true, then the conditional must be true. However, if the conditional is true, the biconditional can be either true or false.

Example in which the Condtional Is True and the Biconditonal Is False

• If A means "all men are mortal" and B means "this man is mortal" then the conditional, A ' B, is true, because if all men are mortal, this man must be. However, the biconditional, A " B, is false, because it is possible that this man is mortal, but some other man is not.