منطقی عامل

منطق میں، منطقی عامل ایک نشان یا لفظ جو دو یا زیادہ جملوں کو قواعد (گرائمر) (رسمی یا قدرتی زبان ) کے مطابق مربوط کرنے کے لیے استعمال کیا جاتا ہے۔ اس طرح کہ مرکب جملے کے معنی کا انحصار اصل جملوں پر ہو۔

فہرست علامات

List of common logical connectives

Commonly used logical connectives include:

• Negation (not): ¬ , Np, ~
• Conjunction (and): $\wedge$ , Kpq, & , ∙
• Disjunction (or): $\lor$, Apq
• Material implication (if...then): $\rightarrow$ , Cpq, $\Rightarrow$ , $\supset$
• Biconditional (if and only if): $\leftrightarrow$ , Epq, $\equiv$ , $=$

Alternative names for biconditional are "iff", "xnor" and "bi-implication".

For example, the meaning of the statements it is raining and I am indoors is transformed when the two are combined with logical connectives:

• It is not raining (

¬P)

• It is raining and I am indoors (P $\wedge$ Q)
• It is raining or I am indoors (P $\lor$ Q)
• If it is raining, then I am indoors (P $\rightarrow$ Q)
• If I am indoors, then it is raining (Q $\rightarrow$ P)
• I am indoors if and only if it is raining (P $\leftrightarrow$ Q)

For statement P = It is raining and Q = I am indoors.

It is also common to consider the always true formula and the always false formula to be connective:

• True formula (⊤, 1, Vpq, or T)
• False formula (⊥, 0, Opq, or F)