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Each logic operator can be used in an assertion about variables and operations, showing a basic rule of inference. Examples: The column-14 operator (OR), shows Addition rule: when p=T (the hypothesis selects the first two lines of the table), we see (at column-14) that p∨q=T.
A truth table has one column for each input variable (for example, A and B), and one final column showing all of the possible results of the logical operation that the table represents (for example, A XOR B). Each row of the truth table contains one possible configuration of the input variables (for instance, A=true, B=false), and the result of ...
An integrated SuperDrive shown on the right side of a MacBook Pro. Once the use of floppy disks started declining, Apple reused the trademark to refer to the optical drives built into its Macintosh models, which could read and write both DVDs and CDs. The early 2001 release of the Power Mac G4 was the first Macintosh to include a SuperDrive. [1]
An example for converse nonimplication in computer science can be found when performing a right outer join on a set of tables from a database, if records not matching the join-condition from the "left" table are being excluded. [3]
Read-once: Can be expressed with conjunction, disjunction, and negation with a single instance of each variable. Balanced: if its truth table contains an equal number of zeros and ones. The Hamming weight of the function is the number of ones in the truth table. Bent: its derivatives are all balanced (the autocorrelation spectrum is zero)
A truth table will contain 2 n rows, where n is the number of variables (e.g. three variables "p", "d", "c" produce 2 3 rows). Each row represents a minterm. Each row represents a minterm. Each minterm can be found on the Hasse diagram, on the Veitch diagram, and on the Karnaugh map.
The self-dual connectives, which are equal to their own de Morgan dual; if the truth values of all variables are reversed, so is the truth value these connectives return, e.g. , maj(p, q, r). The truth-preserving connectives; they return the truth value T under any interpretation that assigns T to all variables, e.g. ∨ , ∧ , ⊤ , → , ↔ ...
For example, the truth table of x 0 in the table of binary operations, namely 2 f 10, has period 2 (and so can be recognized as using only the first variable) even though 12 of the binary operations have period 4. When the period is 2 n the operation only depends on the first n variables, the sense in which the operation is finitary. This ...