SCOPE WORDS

ENGLISH CLUE: scope words

These indicate the left most portion of a sentence which is within the range of an operator. (The right extent of scope sometimes ends with a comma.) In the listing of typical examples, scope words are given in CAPS.

EXAMPLE: Not both oxygen is an element and nitrogen supports combustion, or Art flunked Chemistry.

TRANSLATION: ~(O • N) ∨ F

Note: The NOT goes before the BOTH in English and the ( in symbols since it is not within the scope of the AND .

  BOTH indicates the scope of AND

  IF indicates the scope of THEN

  EITHER indicates the scope of OR

  NEITHER indicates the scope of NOR

  THAT indicates the scope of NECESSARY and also of SUFFICIENT

In the examples that follow, the scope of the first word is shown in bold print.)

EXAMPLE:   If either oxygen or nitrogen are elements then argon is too.
TRANSLATION: (O ∨ N) ⊃ A

EXAMPLE:   Either if oxygen is an element then nitrogen is or argon is too.
TRANSLATION: (O ⊃ N) ∨ A