Converses, inverses and contra positives

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.

Learn with an example

📖 What is the converse of the following conditional?

📖 If Gregory is going to take a lot of notes, then English class is next.

  • If English class is next, then Gregory is going to take a lot of notes.
  • If Gregory is not going to take a lot of notes, then English class is not next.
  • If English class is not next, then Gregory is not going to take a lot of notes.
  • To find the converse of the given conditional, switch the order of the hypothesis and conclusion.
  • If Gregory is going to take a lot of notes, then English class is next.
  • If English class is next, then Gregory is going to take a lot of notes.

📖 What is the contrapositive of the following conditional?

📖 If Miranda is going to buy candy floss, then she is going to Harriet’s candy shop.

  • If Miranda is not going to Harriet’s candy shop, then she is not going to buy candy floss.
  • If Miranda is not going to buy candy floss, then Miranda is not going to Harriet’s candy shop.
  • If Miranda is going to Harriet’s candy shop, then she is going to buy candy floss.
  • To find the contrapositive of the given conditional, switch the order of the hypothesis and conclusion and negate them both.
  • If Miranda is going to buy candy floss, then she is going to Harriet’s candy shop.
  • If Miranda is not going to Harriet’s candy shop, then she is not going to buy candy floss.

📖 What is the contrapositive of the following conditional?

📖 If Miranda is playing wall ball, then it is recess.

  • If Miranda is not playing wall ball, then it is not recess.
  • If it is recess, then Miranda is playing wall ball.
  • If it is not recess, then Miranda is not playing wall ball.
  • To find the contrapositive of the given conditional, switch the order of the hypothesis and conclusion and negate them both.
  • If Miranda is playing wall ball, then it is recess.
  • If it is not recess, then Miranda is not playing wall ball.

Let’s practice!🖊️