: inclusive means `` and/or '' —at least one of the most dreaded subjects of students! is false because when the "if" clause is true, the 'then' clause is false. Statement: We work on Memorial Day if and only if we go to school on Memorial Day. . It is false that P {\displaystyle P} . Tracing the symbol for disjunction. What appears simple often proves more complicated than had been supposed. In logic and mathematics, or is the truth-functional operator of (inclusive) disjunction, also known as alternation;[citation needed] the or of a set of operands is true if and only if one or more of its operands is true. The example above could have been expressed: If you are absent, you have a make up assignment to complete. B " is read as "A or B ". As with other notions formalized in mathematical logic, the meaning of the natural-language coordinating conjunction or is closely related to—but different from—the logical or. Let a represent "We go to school on Memorial Day." Inclusive Disjunction A disjunction p ˅ q false if both disjuncts are false; is otherwise, it is true 2. In logic and mathematics, or is the truth-functional operator of (inclusive) disjunction, also known as alternation; the or of a set of operands is true if and only if one or more of its operands is true. ∨ A single literal is often considered to be a degenerate disjunction. The disjunctive identity is false, which is to say that the or of an expression with false has the same value as the original expression. {\displaystyle A\lor B} Connectives are used to combine the propositions. The logical connective that represents this operator is typically written as ∨ or +. The symbol for this is ν. Examples: Negation inverts the truth or falsehood of logical statements. Such a disjunction is false if both A and B are false. In ordinary language, i.e. Explanation: The if clause is always false (humans are not cats), and the then clause is always true (squares always have corners). (whenever you see $$ Λ $$ , just read 'and') When two simple sentences, p and q, are joined in a conjunction statement, the conjunction is expressed symbolically as p $$ Λ $$ q. The symbol is a logical connector which means "or." (whenever you see ν read 'or') When two simple sentences, p and q, are joined in a disjunction statement, the disjunction is expressed symbolically as p ν q. In Bochvar’s internal three-valued logic, also known as Kleene’s weak three-valued logic, disjunction receives a different interpretation. Statement: If we go to school on Memorial Day, then we work on Memorial Day. Conjunction is a truth-functional connective similar to "and" in English and is represented in symbolic logic with the dot " ". In logic and mathematics, or is the truth-functional operator of (inclusive) disjunction, also known as alternation;[citation needed] the or of a set of operands is true if and only if one or more of its operands is true. {\displaystyle A} The term in logic used to describe the operation commonly known as OR. That means “one or the other” or both. A mathematical sentence is a sentence that states a fact or contains a complete idea. A literal is considered a (degenerate) disjunction (Mendelson 1997, p. 30). A conditional is symbolized like this… More generally a disjunction is a logical formula that can have one or more literals separated only by ORs. In a disjunction statement, the use of OR is inclusive. The only time that a conditional is a false statement is when the if clause is true and the then clause is false . is true if {\displaystyle A} The Wolfram Language command Disjunction[expr, {a1, a2, ...}] gives the disjunction of expr over all choices Note: The word 'then' is optional, and a conditional will often omit the word 'then'. On the other hand, "Her grades are so good that either she's very bright or she studies hard" does not exclude the possibility of both. (See the truth-table at right.) E.g. . Disjunction \color{#D61F06} \textbf{Disjunction} Disjunction. The symbol that is used to represent the OR or logical disjunction operator is \color {red}\Large { \vee } ∨. Logical disjunction is an operation on two logical values, typically the values of two propositions, that has a value of false if and only if both of its operands are false. . The following table documents the most notable of these symbols — along with their respective meaning and example. In logic, a conditional statement is compound sentence that is usually expressed with the key words 'If....then...'. There are five logical operator symbols: tilde, dot, wedge, horseshoe, and triple bar. or . The way I first noticed that the logic symbols weren't standard Unicode was that some logic symbols did not "convert" well to HTML in Course Genie but mysteriously became things like "(". And the entire statement is true. Although the type of a logical disjunction expression is boolean in most languages (and thus can only have the value true or false), in some languages (such as Python and JavaScript), the logical disjunction operator returns one of its operands: the first operand if it evaluates to a true value, and the second operand otherwise. Disjunction is often used for bitwise operations. Although this roughly corresponds to the English expression "Either . in this context, "A or B" is true if A is true, or if B is true, or if both A and B are true. 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