Left side of the arrow
whatever symbol you place to the left of the arrow is the “Sufficient Condition”
Right side of the arrow
whatever symbol you place to the right of it is the “Necessary Condition”.
Like this: [Sufficient Condition] → [Necessary Condition]
Like this: [Sufficient Condition] → [Necessary Condition]
J > F
contrapositive: /F>/J
to create a contrapositive, you flip the symbols and negate
Step 1. Switch the two symbols around the arrow.
Step 2. Slap a negation sign on each symbol.
Step 3. There is no Step 3. It’s a two step process.
be aware of statements that already negated
D > /C
C > /D
You have to remember that when you slap a negation onto a symbol that’s already negated, the negation goes away. Negating “not selfish” becomes “selfish.”
Negation vs Opposition
Contradiction = not (X)
if =
conditional relationship
if > then
dictate a relationship that was given in a sentence.
Group 1: indicators (sufficient)
if, when (whenever), where, all, the only, every, any
Group 2: indicators (necessary)
ONLY, ONLY IF, ONLY WHEN, ONLY WHERE, ALWAYS, MUST, REQUIRE
Group 3: indicators (negate sufficient)
UNLESS, UNTIL, OR, WITHOUT
Or
either or: can be…
inclusive or exclusive
Group 4: indicators
NO, NONE, NOT BOTH, NEVER, CANNOT
- You pick either idea, then negate that idea, then make that idea the necessary condition.
both Group 3 and Group 4 indicators.
You can pick either one to use as logical indicator. The other “logical indicator” becomes a negation.
Unless =
negative
GROUP MISCELLANY
IS ESSENTIAL, IS REQUIRED, IS/ARE
correlation
does not mean causation
Causation made in the premise or conclusion
there is always an error
Co-incidence
two things happening at the same time
A > B
B > A
C > A > B
A > B
B > A
C > A > B