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Understanding Parentheses and Conditional Statements in Logic

This chapter delves into the use of parentheses in logical statements, illustrating how to group statements effectively. Key concepts such as the order of operations (PEMDAS) and truth values of statements like p, q, and r are discussed. Conditional statements, their components (antecedent and consequent), and their symbolic representation are explained with examples. Learn to construct and evaluate conditional statements based on given truth values, enhancing your understanding of logical reasoning.

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Understanding Parentheses and Conditional Statements in Logic

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Presentation Transcript

  1. Chapter 1 Continued http://VIDEO CLIP

  2. Use of Parenthesis • They are used to group statements together • For Example • (p v q) ^ r • p v (q ^ r) • ALSO remember PEMDAS – order of operations, what must be done first?

  3. Remember the statements for p , q , r • p: Santa is jolly • q: Christmas is on July 4th • r: George Washington is the 1st U.S. President • What would be the truth value for (p v q) ^ r • What would be the truth value for p v (q ^ r)

  4. GENERAL TRUTH TABLE for (p v q) ^ r

  5. GENERAL TRUTH TABLE for p v (q ^ r)

  6. TRY THIS • p: true • q: true • r : false • Find the truth value for the statement below [p v (q ^ r)] v ~ q

  7. Lets do a ANOTHER Truth Table (p ^ q) v r

  8. Lets do a ANOTHER Truth Tablep ^ (q v r)

  9. Conditional Statement • Is a statement that is true unless p is true and q is false • p is called the antecedent (comes before something else) • q is called the consequent ( the result) • Can also be called the hypothesis and the conclusion • Symbol for conditional statement is an arrow  • p  q is read as “if p then q”

  10. EXAMPLES OF Conditional Statements Let p be the sentence “Santa is Jolly” Let q be the sentence “ Christmas is on July 4th” Let r be the sentence “George Washington was the first U.S. President: Write a conditional statement of p and q Write a conditional statement of p and r Write a conditional statement of q and r

  11. Check your AnSwErS • p  q is “ If Santa is jolly, then Christmas is on July 4th • q  r is “ If Christmas is on July 4th, then George Washington is the 1st US President • p  r is “If Santa is jolly, then George Washington is the 1st US President

  12. Try Conditionals & Negations • ~ p  q • ~q  r • p  ~q

  13. Check your Answers • ~ p  q “If Santa is not jolly, then Christmas is on July 4th” • ~q  r “If Christmas is not on July 4th, then George Washington is the 1st US President • p  ~q “If Santa is jolly, then Christmas is not on July 4th

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