Logic Operations and Properties

• Properties of individual operations (=,^,V,->)
• reflexive, symmetric, transitivity
• Associative

• Knockout

  • T^A = A
  • F^A = F
  • TVA = T
  • FVA = A
  • ??? There is some 'flipped' nature here A B A&B A|B T T T T T F F T F T F T F F F F

• DEF Subsitution A=B -> A@C=B@C

• A^B -> A,B
• A^!A = F
• AV!A = T

??? What comes first? sub or eq? also the definition of = uses -> = between values = between functions = between variables what are variables? a function with variables f(A,B) is a variable (I keep thinking back to the table, its such a concrete way to represent the variable space)

• DEF var=var
  • A=B means
    • If A is true then B is true ^ If B is true then A is true
    • This is identical to <->
    • Another way is A True means B True, A False then B False
  • From the defintion, we can see A=A, A=B->B=A, and A=B,B=C->A=C