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Conditional and Biconditional Statements

Conditional and Biconditional Statements

Conditional and Biconditional Statements Video

In this video, you will learn that a conditional statement, symbolized by pq, 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.

Loaf of breadPlease buy a loaf of bread if you go to the store today.

Hypothesis:
you go to the store today
Conclusion:
please buy a loaf of bread
Conditional:
If you go to the store today, then please buy a loaf of bread.


Woman waiting in lineStep forward when it is your turn.

Hypothesis:
it is your turn
Conclusion:
step forward
Conditional:
If it is your turn, then step forward.


Purchasing two concert ticketsYou can attend the concert only if you have purchased a ticket.

Hypothesis:
you have purchased a ticket
Conclusion:
you can attend the concert
Conditional:
If you have purchased a ticket, then you can attend the concert.

 

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).

Conditional pq: If a number is even, then the number is divisible by 2. (The conditional statement is valid.)

Converse qp: If a number is divisible by 2, then the number is even. (The converse is valid.)

Both the conditional statement and its converse are valid. Therefore, the biconditional statement is valid.

 

Conditional and Biconditional Statements Review

Conditional and Biconditional Statements Review Interactivity

Review iconNow that you have learned about conditional and biconditional statements, review your knowledge in this interactivity. Click the player button to get started.