If – Then Statements Lesson 1.5.

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Presentation transcript:

If – Then Statements Lesson 1.5

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: p q means p  q and q  p

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

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

Contrapositive, Converse, Inverse of a Statement Given Conditional Its Contrapositive Its Converse Its Inverse p  q ~ q  ~ p q  p ~ p  ~ q

Cars Conditional: If a car is a neon, then it is a Dodge. 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

Statement: the conditional has the same truth value as its contrapositive. Proof: P Q P  Q ~Q ~P ~Q  ~P T F P Q P  Q ~Q ~P ~Q  ~P

Try one! Write the contrapositive, converse, and inverse 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. A A A A

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