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What is necessary and sufficient condition in logic?
A necessary condition is a condition that must be present for an event to occur. A sufficient condition is a condition or set of conditions that will produce the event. A necessary condition must be there, but it alone does not provide sufficient cause for the occurrence of the event.
What does necessary mean in logic?
A sufficient condition guarantees the truth of another condition, but is not necessary for that other condition to happen. A necessary condition is required for something else to happen, but it does not guarantee that the something else happens.
What is the difference between necessary and sufficient conditions examples?
For example, while air is a necessary condition for human life, it is by no means a sufficient condition, i.e. it does not, by itself, i.e. alone, suffice for human life.
Can something be sufficient but not necessary?
A sufficient condition is only one of the means to achieve a particular outcome. This means that there could be other means to achieve the outcome. Therefore, a sufficient condition is not necessary to be fulfilled in order to achieve the desired outcome.
What does sufficient mean in logic?
In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements. In general, a necessary condition is one that must be present in order for another condition to occur, while a sufficient condition is one that produces the said condition.
What is an example of sufficient?
The definition of sufficient is enough or as much as is needed. An example of sufficient is when you have just enough food. Possessing adequate talents or accomplishments; of competent power or ability; qualified; fit. A two-week training course is sufficient to get a job in the coach-driving profession.
What is the symbol of if and only if?
Basic logic symbols
| Symbol | Name | Read as |
|---|---|---|
| ⇔ ≡ ↔ | material equivalence | if and only if; iff; means the same as |
| ¬ ˜ ! | negation | not |
| Domain of discourse | Domain of predicate | |
| ∧ · & | logical conjunction | and |
What is a sufficient cause?
Rothman defined a sufficient cause as “…a complete causal mechanism” that “inevitably produces disease.” Consequently, a “sufficient cause” is not a single factor, but a minimum set of factors and circumstances that, if present in a given individual, will produce the disease.
How do you prove necessary and sufficient?
The assertion that a statement is a “necessary and sufficient” condition of another means that the former statement is true if and only if the latter is true. That is, the two statements must be either simultaneously true, or simultaneously false.
Is only if sufficient or necessary?
It’s important to remember that “only,” “only if,” and “only when” all introduce the necessary condition. These “necessary condition prompters” should not be clumped together with the notorious “the only.” “The only” will introduce the sufficient condition.