USING THE LAWS OF LOGIC

1
USING THE LAWS OF LOGIC

• WORKING WITH NEGATING A STATEMENT THE
  COUNTRAPOSITVE OF A CONDITIONAL STATEMENT
• HOW TO USE SYLLOGISM

2
COUNTRAPOSITIVES

• REMEMBER HYPOTHESIS IS p AND CONCLUSION IS q.
• STATEMENT, p THE RIDE IS FUN NEGATION, p THE
  RIDE IS NOT FUN.
• COUNTRAPOSITIVE qgtp
• COUNTRAPOSITIVE IS TRUE IF THE ORIGINAL STATEMENT
  IS TRUE

3
WRITING A COUNTRAPOSITIVE

• pgtq IF THE RIDE IS FUN, THEN I WILL RIDE IT
  AGAIN.
• qgtp IF I DO NOT RIDE IT AGAIN, THEN THE RIDE
  WAS NOT FUN.

4
CONVERSE qgtp

• IF I RIDE IT AGAIN, THEN THE RIDE WAS FUN.
• THE TRUTH OR FALSITY OF THE ORIGINAL STATEMENT
  HAS NO BEARING ON THE T/F OF THE CONVERSE

5
LAW OF SYLLOGISM

• LIKE THE TRANSITIVE RULES
• pgtq
• qgtr
• THEREFORE, pgtr

6
EXAMPLE

• IF I STUDY HARD, THEN I DO WELL IN CLASS.
• IF I DO WELL IN CLASS, THEN I AM HAPPY
• IF ISTUDY HARD THEN I AM HAPPY

7
LAW OF DETACHMENT

• LIKE THE REFLEXIVE PROPERTY OF EQUALITY
• pgtq
• p IS TRUE
• THEREFORE, q IS TRUE