Rewriting Definitions as Biconditionals

In this activity, you will explore how a definition can be written as a biconditional.

  1. On the STANDARD tab, with Rewriting definitions as biconditionals selected in the dropdown menu, read the given definition.
    1. What word is being defined? What is the definition given?
    2. On paper, restate the given definition as a conditional. Then give the converse of that conditional. Are these both true?
    3. Combine the two conditionals you wrote in the previous question into one biconditional statement. Remember, a biconditional should contain the phrase "if and only if" in the middle of it.
    4. Form the biconditional in the Gizmotm by dragging the word tiles into the Biconditional statement bin. Do not worry about capitalization or punctuation.
    5. Click Check and read the given feedback. Is your answer correct? If not, change your answer and click Check again. To start over on the given question, click Reset.
  2. With Rewriting definitions as biconditionals selected in the dropdown menu, click on the SYMBOLIC tab.
    1. What does the symbol double arrow mean?
    2. Write a biconditional statement that means the same thing as the given definition.
    3. Drag the appropriate word tiles into the p bin and the q bin to form the biconditional that is equivalent to the definition. Both p and q should be complete sentences. (Hint: The first two words of both p and q should be the same. Do not use the word "it" at the beginning of q.) Again, do not worry about capitalization or punctuation. Click Check to check your answer.
  3. Click New for more practice with rewriting definitions as biconditionals. Practice with both standard form and symbolic form.

Writing Biconditionals

In this activity, you will combine a conditional and its converse to form an equivalent biconditional.

  1. Click on the STANDARD tab and select Writing biconditionals. Read the two given statements.
    1. What are the two given conditionals? How does Statement 2 relate to Statement 1? Are both statements true?
    2. What is the biconditional statement that combines both of the given statements? Be sure your biconditional contains the phrase "if and only if." Form that biconditional by placing word tiles into the Biconditional statement bin, and then click Check. Is your answer correct?
  2. With Writing biconditionals selected, click on the SYMBOLIC tab.
    1. How is the given statement in symbolic form different from the given statements in standard form?
    2. Form the biconditional sentence that is equivalent to the given statements in the Biconditional statement bin using word tiles. Click Check to check your answer.
  3. Click New to practice writing biconditionals. Practice with both standard and symbolic form.

Rewriting Biconditionals as Two Conditionals

In this activity, you will take a biconditional and break it down into its components, a conditional and its converse.

  1. Click on the STANDARD tab and select Rewriting biconditionals as two conditionals. Read the given biconditional.
    1. A biconditional is a conditional combined with its converse. What conditional and converse were combined to make the given biconditional?
    2. Use the word tiles to form the conditional in the Conditional bin and the converse in the Converse bin. Click Check. Are your answers correct?
    3. What is the converse of the converse? If you reversed your answers in the two bins, do you think that would also be correct? Explain.
  2. With Rewriting biconditionals as two conditionals selected, click on the SYMBOLIC tab.
    1. What is the given statement in symbolic form? What was the given statement in standard form? Explain why these mean the same thing.
    2. Use the word tiles to form p right arrow q in the p right arrow q bin and q right arrow p in the q right arrow p bin. Click Check. Are your answers correct?
    3. Explain why it would be incorrect to reverse your answers in the two bins in this case.
  3. Click New for more practice rewriting biconditionals as two conditionals. Practice both standard and symbolic form.