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Conditional and Biconditional Statements in Mathematics

Explore the concepts of conditional and biconditional statements in mathematics. Learn how hypotheses and conclusions are defined and their applications through examples. Understand the difference between if-then statements and if-and-only-if statements. Enhance your mathematical reasoning skills in logical statements.

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Conditional and Biconditional Statements in Mathematics

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  1. Conditional & Biconditional Chapter 3 section 3

  2. Conditional • The p is called the hypothesis and the q is called the conclusion.

  3. Examples • I am an owner of a small factory, a rush order must be filled out by Monday. I approach you with this generous offer: • p = You work for me on Saturday. • q = I’ll give you a $100 bonus. • If you work for me on Sat., then I’ll will give you a $100 bonus.

  4. Case 1 • You come to work and you receive the bonus. • If p is true and q is true. • Case 2 • You come to work and you don’t receive the bonus. • If p is true then q is false.

  5. Case 3 • You don’t come to work, but I will give you a bonus. • If p is false, then q is true. • Case 4 • You don’t come to work and you don’t receive the bonus. • If p is false, then q is false.

  6. Case 3 explaination • Do you understand why? • In mathematics we tend to use if…then statements a little different. Do not read more into my statement. You do not expect to get the bonus if you did not come to work because that is your experience. I never said that. You are assuming this condition.

  7. Biconditional • Iff- if and only if. • It means that two statements say the same thing.

  8. Examples • x+3 = 7 iff x = 4 • Today is Monday iff tomorrow is Tuesday.

  9. Table

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