Question

Identify the category of the following formula:

~(D→E)&(FvG)
A) Conjunction
B) Disjunction
C) Negation
D) Conditional

Answer 1

The formula ~ (D → E)&(FvG) is categorized as a conjunction because it combines a negation of a conditional statement and a disjunction with the logical 'AND' symbol.

Step-by-step explanation:

The formula ~(D→E)&(FvG) falls into multiple logical categories: negation, conjunction, disjunction, and conditional. Breaking it down:

• ~(D→E) represents a negation of a conditional statement. '~' is the symbol for negation, and '→' represents a conditional relationship or 'implies'.
• (D→E) in itself, without the negation, is a conditional statement.
• (FvG) is a disjunction, where 'v' symbolizes the logical 'OR'.
• The entire formula ~(D→E)&(FvG) is a conjunction because of the '&' symbol tying the two parts together, which represents the logical 'AND'.

Given these pieces, the overall category of the formula is a conjunction, despite it containing elements of negation, disjunction, and conditional within it.