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Draw a logic network and input-output table for the following: p ^ ( q v ~r)

Draw a logic network and input-output table for the following: p ^ ( q v ~r). If – Then Statements. Lesson 1.5. Goals for the day: Apply the ideas of formal logic from previous lessons to the treatment of the truth values of a universal conditional and its negation. .

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Draw a logic network and input-output table for the following: p ^ ( q v ~r)

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  1. Draw a logic network and input-output table for the following: p ^ ( q v ~r)

  2. If – Then Statements Lesson 1.5 Goals for the day: Apply the ideas of formal logic from previous lessons to the treatment of the truth values of a universal conditional and its negation.

  3. If it rains today, then we will not go to the pool. If p then q is called a Conditional Statement (sometimes shown as p  q or as “p implies q”) p is the input, hypothesis, antecedent q is the output, conclusion, consequent Biconditional: pq means p  q and q  p

  4. Truth Table for p  q ** The one to pay attention to is F  T ; because there is no counterexample, this statement is true.

  5. p  q p  q has the same truth value as ~p v q Since this is true, the negation for this is?? p ^ ~ q (deMorgan’s Law!) If it is snowing today, then we will not have school. Negation: It is snowing today and we do have school!

  6. Example 1 Give the truth value of the conditional. If 4 > 9, then 4 > 7 If 6 < 8, then 6 < 10 If 5 < 3, then 5 < 9 False  False; truth value: True True  True; truth value: True False  True; truth value: True

  7. Contrapositive, Converse, Inverse of a Statement

  8. Neons Conditional: If a car is a neon, then it is a Dodge. Contrapositive: If the car is not a dodge, then it is not a neon. Converse: If the car is a dodge, then it is a neon. (false) Inverse: If the car is not a neon, then it is not a dodge. (false) Dodge Cars

  9. Statement: the conditional has the same truth value as its contrapositive. Proof:

  10. Try one! Write the contrapositive, converse, inverse, and negation of the universal conditional: functions f, if f is a logarithm function, then f(1) = 0. Contrapositive: functions f, If f(1) ≠ 0, then f is not a logarithm function. Converse: functions f, If f(1) = 0, then f is a logarithm function. Inverse: functions f, If f is not a logarithm function, then f(1) ≠ 0. Negation: a function f st f is a logarithm function and f(1) ≠ 0 A A A A E

  11. Homework Page 45 2-22(evens) 24: extra credit!

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