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Compound Statements

Compound Statements. Lesson 1.3. 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. Truth Table. Other definitions.

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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