How Do We Review Logic?

Knowing all from what is logic to the biconditional, we are ready to perform some examples and review what have we learned so far.


Logic
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Mathematical Sentence

• 17 - 5 = 12 ------------> T

• 17 +3 = 42 ------------> F

• 0.1 < 1 -----------------> T

Conditional
REMEMBER:

IF...THEN is only FALSEwhen
T implies F.
All other cases are TRUE.

Inverse

• "If it is not raining, then it is not cloudy"
• "If twice Talia's age is not 10, then Talia is not 5 years old"

REMEMBER: Under negation, TRUE becomes FALSE - or - FALSE becomes TRUE. Converse Conditional:  "If the space shuttle was launched, then a cloud of smoke was seen." Converse:      "If a cloud of smoke was seen, then the space shuttle was launched." HINT:  Try to associate the logical CONVERSE with Converse™ sneakers -- think of the two parts of the sentence "putting on their sneakers" and "running" to their new positions. Contrapositive HINT:  Remember that the contrapositive (a big long word) is really the combining together of the strategies of two other words:  converse and inverse. An important fact to remember about the contrapositive, is that it always has the SAME truth value as the original conditional statement. **If the original statement is TRUE, the contrapositive is TRUE.   If the original statement is FALSE, the contrapositive is FALSE. They are said to be logically equivalent. Biconditional REMEMBER: IF AND ONLY IF is TRUE   when both facts are T  or both facts are F.. Problem 1. Which of the following statements is the converse of"If the moon is full, then the vampires are prowling."? Choose one:  If the vampires are prowling, then the moon is full.  If the moon is not full, then the vampires are  prowling.  If the vampires are not prowling, then the moon is not full. **Images and Examples provided by regentsprep.org and my notes from Geometry class.