False Value: Book 8 in the #1 bestselling Rivers of London series (A Rivers of London novel)

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For binary operators, a condensed form of truth table is also used, where the row headings and the column headings specify the operands and the table cells specify the result. For example, Boolean logic uses this condensed truth table notation: Truth tables can be used to prove many other logical equivalences. For example, consider the following truth table:

Logical negation is an operation on one logical value, typically the value of a proposition, that produces a value of true if its operand is false and a value of false if its operand is true. The logical NOR is an operation on two logical values, typically the values of two propositions, that produces a value of true if both of its operands are false. In other words, it produces a value of false if at least one of its operands is true. ↓ is also known as the Peirce arrow after its inventor, Charles Sanders Peirce, and is a Sole sufficient operator. Exclusive disjunction is an operation on two logical values, typically the values of two propositions, that produces a value of true if one but not both of its operands is true. The negation of a conjunction: ¬( p∧ q), and the disjunction of negations: (¬ p)∨(¬ q) can be tabulated as follows: Logical equality (also known as biconditional or exclusive nor) is an operation on two logical values, typically the values of two propositions, that produces a value of true if both operands are false or both operands are true.The output value is never true: that is, always false, because this operator has zero operands and therefore no input values IFS(logical_test1, value_if_true1, [logical_test2, value_if_true2], [logical_test3, value_if_true3],…) The logical NAND is an operation on two logical values, typically the values of two propositions, that produces a value of false if both of its operands are true. In other words, it produces a value of true if at least one of its operands is false.

Here is an extended truth table giving definitions of all sixteen possible truth functions of two Boolean variables p and q: [note 1] p

In ordinary language terms, if both p and q are true, then the conjunction p ∧ q is true. For all other assignments of logical values to p and to q the conjunction p∧ q is false.

Use the IF function along with AND, OR and NOT to perform multiple evaluations if conditions are True or False.IF A2 (25) is greater than 0, AND B2 (75) is less than 100, then return TRUE, otherwise return FALSE. In this case both conditions are true, so TRUE is returned. 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 the operation for those values. The truth table associated with the material conditional if p then q (symbolized as p→q) is as follows:

Result to be returned if logical_testN evaluates to TRUE. Each value_if_trueN corresponds with a condition logical_testN. Can be empty.Truth tables are also used to specify the function of hardware look-up tables (LUTs) in digital logic circuitry. For an n-input LUT, the truth table will have 2