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In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements. For example, in the conditional statement : "If P then Q ", Q is necessary for P , because the truth of Q is guaranteed by the truth of P .
The detailed semantics of "the" ternary operator as well as its syntax differs significantly from language to language. A top level distinction from one language to another is whether the expressions permit side effects (as in most procedural languages) and whether the language provides short-circuit evaluation semantics, whereby only the selected expression is evaluated (most standard ...
If-then-else flow diagram A nested if–then–else flow diagram. In computer science, conditionals (that is, conditional statements, conditional expressions and conditional constructs) are programming language constructs that perform different computations or actions or return different values depending on the value of a Boolean expression, called a condition.
expression 1, expression 2: Expressions with values of any type. If the condition is evaluated to true, the expression 1 will be evaluated. If the condition is evaluated to false, the expression 2 will be evaluated. It should be read as: "If condition is true, assign the value of expression 1 to result.
A conditional statement may refer to: A conditional formula in logic and mathematics, which can be interpreted as: Material conditional; Strict conditional; Variably strict conditional; Relevance conditional; A conditional sentence in natural language, including: Indicative conditional; Counterfactual conditional; Biscuit conditional
Observe that we have four right-angled triangles and a square packed into a larger square. Each of the triangles has sides a and b and hypotenuse c. The area of a square is defined as the square of the length of its sides. In this case, the area of the large square is (a + b) 2. However, the area of the large square can also be expressed as the ...
In propositional logic, material implication [1] [2] is a valid rule of replacement that allows a conditional statement to be replaced by a disjunction in which the antecedent is negated. The rule states that P implies Q is logically equivalent to not-or and that either form can replace the other in logical proofs.
The name denying the antecedent derives from the premise "not P", which denies the "if" clause (antecedent) of the conditional premise. The only situation where one may deny the antecedent would be if the antecedent and consequent represent the same proposition, in which case the argument is trivially valid (and it would beg the question ...