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Conditional Statements, a la Shmoop Some statements we make are more than just

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statements of fact or fiction.

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Like… “Grandma, you look incredible after your makeover.” Who’s to say which category

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that particular statement belongs to?

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Some statements are conditional.

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Conditional statements are "If-Then" statements that have two parts: a hypothesis and conclusion.

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The hypothesis comes after the "if" and tells us the condition that must be satisfied. The

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conclusion comes after the "then" and tells us what happens if the hypothesis is true.

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They usually take the form: "If hypothesis, then conclusion."

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"If I do well on all my tests, then I will get all A's this semester."

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"If it walks like a duck and quacks like a duck, then it's probably a duck."

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"If you liked it, then you should have put a ring on it."

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Keep in mind that a conditional statement is only applicable if the hypothesis is true.

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If you liked it, then you should have put a ring on it.

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But we can't tell you what you should or shouldn't have done if you didn't like it. That's for

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Beyoncé to decide. Of course, mathematicians prefer numbers and

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symbols to long and complicated sentences…

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…so they came up with a way of representing conditional statements in a different way.

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The statement "If hypothesis P, then conclusion Q" can represented by drawing an arrow from

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P to Q. But not all conditional statements take the

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"If-Then" form.

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Some of them might look like, "All hypothesis conclusion" or "Conclusion whenever hypothesis."

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Sneaky little devils.

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How can we write, "All dogs go to heaven" in P Q form?

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First, let's write it as an If-Then statement.

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All dogs go to heaven means that…

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…if we're talking about a dog, then it will go to heaven.

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We want to put that statement into P Q form, which looks like this.

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So really, all we need to do is replace our P with our hypothesis and Q with our conclusion.

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Since our statement is, "If it is a dog, then it will go to heaven"…

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…our hypothesis is, "It is a dog"…

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…and our conclusion is, "it will go to heaven."

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Draw an arrow in between them, and we've done it. We can even condense it further and maybe

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save a few trees. We have one last conditional statement for

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you before you go.

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IF you learned something from this video, THEN you just got a little bit smarter.

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We did say a little bit.

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