Conditional and Biconditional Statements
In this video, you will learn that a conditional statement, symbolized by p → q, is an if-then statement in which p represents the hypothesis and q represents the conclusion. You will also learn how to modify a conditional statement to write different types of logic statements. Click the player button to begin.
View a transcript of this video.
Conditional statements may not always be written in standard if-then form; however, you can write a conditional statement in standard form by identifying its hypothesis and conclusion. Remember: The conclusion always depends on the hypothesis.
Hover your mouse over each rectangle below to reveal the hypothesis, conclusion, and standard form of each conditional statement.
Please buy a loaf of bread if you go to the store today.
Hypothesis:
Conclusion:
Conditional:
Step forward when it is your turn.
Hypothesis:
Conclusion:
Conditional:
You can attend the concert only if you have purchased a ticket.
Hypothesis:
Conclusion:
Conditional:
More on Biconditional Statements
Is the biconditional statement below valid?
A number is even if and only if the number is divisible by 2.
To determine if a biconditional statement is valid, determine if the corresponding conditional statement and converse are both valid.
Given biconditional: A number is even if and only if the number is divisible by 2.
Notice that the italicized clause "a number is even" is the hypothesis (represented by p below) and the italicized clause "the number is divisible by 2" is the conclusion (represented by q below).
Now that you have learned about conditional and biconditional statements, review your knowledge in this interactivity. Click the player button to get started.