'''Note.''' Many writers draw a technical distinction between the form "<math>p\!</math> implies <math>q\!</math>" and the form "if <math>p\!</math> then <math>q\!</math>". In this usage, writing "<math>p\!</math> implies <math>q\!</math>" asserts the existence of a certain relation between the logical value of <math>p\!</math> and the logical value of <math>q\!</math> while writing "if <math>p\!</math> then <math>q\!</math>" merely forms a compound statement whose logical value is a function of the logical values of <math>p\!</math> and <math>q\!</math>. This will be discussed in detail below. | '''Note.''' Many writers draw a technical distinction between the form "<math>p\!</math> implies <math>q\!</math>" and the form "if <math>p\!</math> then <math>q\!</math>". In this usage, writing "<math>p\!</math> implies <math>q\!</math>" asserts the existence of a certain relation between the logical value of <math>p\!</math> and the logical value of <math>q\!</math> while writing "if <math>p\!</math> then <math>q\!</math>" merely forms a compound statement whose logical value is a function of the logical values of <math>p\!</math> and <math>q\!</math>. This will be discussed in detail below. |