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Logic Reasoning 6

Conditional Reasoning- sufficient and necessary

TermDefinition
sufficient condition an even or circumstance whose occurrence indicates that a necessary condition must also occur
necessary condition an event or circumstance whose occurrence is required in order for a sufficient condition to occur
if there is a sufficient condition... there has to be a necessary condition
if there is a necessary condition... doesn't mean anything
logical feature #1 1) sufficient doesn't MAKE necessary occur
logical feature #2 either can occur first or can occur at same time
logical feature #3 relationship doesn't have to reflect reality
Original to contra-positive, A -> B not B -> not A
Original to contra-positive, C -> not D D -> not C
contra-positive reversed and negated, so valid
if sufficient indicator
when sufficient indicator
whenever sufficient indicator
every sufficient indicator
all sufficient indicator
any sufficient indicator
people who sufficient indicator
in order to sufficient indicator
then necessary indicator
only necessary indicator
only if necessary indicator
must necessary indicator
required necessary indicator
unless necessary indicator
except necessary indicator
until necessary indicator
without necessary indicator
"unless, expect, until, without" whatever is modified by "unless, expect, until, without" becomes necessary, remaining term is negated and sufficient
"Unless they study, they won't get an A+." sufficient = get A+ necessary = study
"no, none" modifies necessary condition
"No robot can think." Actually means... All robots cannot think. "If robot, then can't think."
"only way" only modifies way
"The only way to achieve success is to work hard." sufficient = achieve success necessary = work hard "To achieve success, the only way is to work hard."
"either/or" at least one of the two, possible both
Multiple contra-positive replaces "and" with "or" and vice versa
"To graduate from college you must be both smart and resourceful." sufficient = graduate necessary = smart AND resourceful contra- sufficient = not smart OR not resourceful contra-necessary = not graduate
Double arrow, "if and only if" each term is both sufficient and necessary for the other
Double NOT arrow two terms cannot occur together
Created by: mrshelley