Biconditionals

Key Notes:

📚 A conditional statement can be written as If A, then B. A is the hypothesis and B is the conclusion.

📚 The converse of the conditional If A, then B is If B, then A. The hypothesis and conclusion are switched.

📚 A biconditional is a statement that combines a conditional and its converse. Biconditionals are frequently written in the form A if and only if B.

Learn with an example

✈️ Is the following statement a biconditional?

✈️ Michael smiles if and only if he sees clowns perform.

  • yes
  • no
  • Look at the given statement:
    Michael smiles if and only if he sees clowns perform.
  • The given statement is a biconditional because it is equivalent to the following two statements:
  • If Michael smiles, then he sees clowns perform.
  • If Michael sees clowns perform, then he smiles.

✈️ Is the following statement a biconditional?

✈️ If it is Tuesday, then Maya has a sandwich for lunch.

  • yes
  • no
  • Look at the given statement:
  • If it is Tuesday, then Maya has a sandwich for lunch.
  • A biconditional says that both a conditional and its converse are true. The given statement is only a conditional, not a biconditional.

✈️ Is the following statement a biconditional?

✈️ If Ford is excited, then spelling class is next.

  • yes
  • no
  • Look at the given statement:
  • If Ford is excited, then spelling class is next.
  • A biconditional says that both a conditional and its converse are true. The given statement is only a conditional, not a biconditional.

Let’s practice!🖊️