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Compound Statements

This lesson explores compound statements using AND and OR logic, crucial in mathematics and computer science. We learn that a statement P and Q is true only when both P and Q are true (symbol: ^) and that a statement P or Q is true if at least one is true (symbol: V). The lesson also distinguishes between exclusive or (choosing one but not the other) and inclusive or (choosing one or both). It includes solving inequalities and applying De Morgan’s Laws for negating compound statements. Practice solving and graphing is provided.

beverly-leblanc
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Compound Statements

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  1. Compound Statements Lesson 1.3

  2. And and or Statements • P and Q  The statement p and q is true when, and only when, only p and q are true. Symbol: ^ • P or Q  The statement p or q is true when either p is true or q is true. Symbol: V

  3. Truth Table

  4. Other definitions • Exclusive or: If you choose one, you will not want the other -Example: Would you like a cup of tea or a cup of coffee? • Inclusive or: You may choose either or both of these choices. -Example: Would you like cream or sugar?

  5. Examples - AND • Solve and graph the solution set: |x – 3| ≤ 15 x – 3 ≤ 15 x – 3 ≥ -15 x ≤ 18 x ≥ -12 -12 18 0

  6. Example 2 - OR • Solve and Graph the solution set: 7 – x > 10 or 12 ≤ 6x 7 – x > 10 12 ≤ 6x -x > 3 x < 3 2 ≤ x 2 3

  7. De Morgan’s Laws • For all statements p and q: • ~(p and q) Ξ ~p or ~q ~(p ^ q) Ξ ~p v ~q • ~(p or q) Ξ ~p and ~q ~(p v q) Ξ ~p ^ ~q

  8. Proving De Morgan’s First Law: ~(p and q) Ξ ~ p or ~ q

  9. Homework Page 27 -29 2 – 24

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