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Rogers (1957; 1959) stated that there are six necessary and sufficient conditions required for therapeutic change: [6]: 142–143 Therapist–client psychological contact: A relationship between client and therapist must exist, and it must be a relationship in which each person's perception of the other is important.
A condition can be both necessary and sufficient. For example, at present, "today is the Fourth of July" is a necessary and sufficient condition for "today is Independence Day in the United States". Similarly, a necessary and sufficient condition for invertibility of a matrix M is that M has a nonzero determinant.
The absence these conditions guarantees the outcome cannot occur, and no other condition can overcome the lack of this condition. Further, necessary conditions are not always sufficient. For example, AIDS necessitates HIV, but HIV does not always cause AIDS. In such instances, the condition demonstrates its necessity but lacks sufficiency.
It is a necessary condition that an object has four sides if it is true that it is a square; conversely, the object being a square is a sufficient condition for it to be true that an object has four sides. [4] Four distinct combinations of necessity and sufficiency are possible for a relationship of two conditions. A first condition may be:
Causes may sometimes be distinguished into two types: necessary and sufficient. [19] A third type of causation, which requires neither necessity nor sufficiency, but which contributes to the effect, is called a "contributory cause". Necessary causes If x is a necessary cause of y, then the presence of y necessarily implies the prior occurrence ...
The necessary conditions are sufficient for optimality if the objective function of a maximization problem is a differentiable concave function, the inequality constraints are differentiable convex functions, the equality constraints are affine functions, and Slater's condition holds. [11]
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