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compound statement A statement in logic that is formed by combining two or more statements with logical connectives, allowing for the construction of more complex statements from simpler ones. [67] [68] comprehension schema A principle in set theory and logic allowing for the formation of sets based on a defining property or condition.
Wherever logic is applied, especially in mathematical discussions, it has the same meaning as above: it is an abbreviation for if and only if, indicating that one statement is both necessary and sufficient for the other. This is an example of mathematical jargon (although, as noted above, if is more often used than iff in statements of definition).
A statement is regarded as the information content of an information-bearing sentence. Thus, a sentence is related to the statement it bears like a numeral to the number it refers to. Statements are abstract logical entities , while sentences are grammatical entities .
If a statement's inverse is false, then its converse is false (and vice versa). If a statement's negation is false, then the statement is true (and vice versa). If a statement (or its contrapositive) and the inverse (or the converse) are both true or both false, then it is known as a logical biconditional.
Logical reasoning is a form of thinking that is concerned with arriving at a conclusion in a rigorous way. [1] This happens in the form of inferences by transforming the information present in a set of premises to reach a conclusion.
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 .
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.
The following statements are examples of false equivalence: [3] "The Deepwater Horizon oil spill is no more harmful than when your neighbor drips some oil on the ground when changing his car's oil." The "false equivalence" is the comparison between things differing by many orders of magnitude: [ 3 ] Deepwater Horizon spilled 210 million US gal ...