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Understanding Conditional Statements in Mathematics

This guide covers the basics of conditional statements in mathematics, focusing on the structure of "if-then" propositions. Key components include the hypothesis (the "if" part) and the conclusion (the "then" part), with examples illustrating how to identify and work with these concepts. You'll learn about conversions between conditions, including converse, inverse, and contrapositive. Additionally, the law of syllogism is discussed through engaging real-world examples. Perfect for students aiming to strengthen their understanding of logical reasoning in math.

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Understanding Conditional Statements in Mathematics

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  1. AIMS Math Prep Conditional Statements

  2. Conditional Statements • A conditional statement includes an “if” and “then” part. • The “if” part is called the hypothesis. • The “then” part is called the conclusion. • For a conditional statement to be true, when the hypothesis is true, the conclusion must also be true.

  3. Example 1 • Underline the hypothesis and double underline the conclusion. • If you attend Vista Grande High School, then you are a Spartan.

  4. Example 1 Solution • Underline the hypothesis and double underline the conclusion. • If you attend Vista Grande High School, then you are a Spartan.

  5. Conditional Statements • Converse • Switch the hypothesis and conclusion • Inverse • Make both the hypothesis and conclusion negative (usually use the word “not”. • Contrapositive • Switch the hypothesis and conclusion and make both parts negative.

  6. Example 2 • Write the converse, inverse and contrapositive. • If you attend Vista Grande High School, then you are a Spartan.

  7. Example 2- Solutions • Write the converse, inverse and contrapositive. • If you attend Vista Grande High School, then you are a Spartan. • Converse • If you are a Spartan, then you attend Vista Grande High School. • Inverse • If you do not attend VGHS, then you are not a Spartan. • Contrapositive • If you are not a Spartan, then you do not go to VGHS.

  8. Example 3

  9. Example 3 Solution

  10. Example 4

  11. Example 4 Solution

  12. Law of Syllogism

  13. Examples • Recently these commercials have been on TV. They illustrate the law of syllogism. • http://www.youtube.com/watch?v=7udQSHWpL88 • A response posted about this commercial: • When you watch this commercial, you get DirectTV • When you get DirectTV, you pay too much for it • When you pay too much for it, you go broke • When you go broke, you end up homeless • When you end up homeless, you go live under bridges • When you live under bridges, you get attacked by trolls • When you get attacked by trolls, you're in Skyrim • When you're in Skyrim, you take an arrow to the knee • Don't take an arrow to the knee, get rid of DirectTV and go back to cable

  14. Another Commercial • http://youtu.be/CCuPyLeDzng

  15. Example 5

  16. Example 5 Solution

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