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Logic Reasoning 6
Conditional Reasoning- sufficient and necessary
| Term | Definition |
|---|---|
| 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 |