Consider the following set of TL sentences g is B some B

Consider the following set, , of TL sentences. = { g is B , some B are not B , l is B , l is g , g is g } (a) [3 points ] . has six non - similar TL diagrams. Draw all of them [0.25 pt each] and determine the truth values of ’s members in each TL diagram [0.25 pt each] . Use these TL diagrams to answer the following questions : (b) Is the set consistent [0.25 pt] ? Why [0.25 pt] ? (c) Are ‘ g is B ’ and ‘ l is B ’ logically equivalent [0.25 pt] ? Why [0.25 pt] ? (d) Is ‘ g is B ’ a logical consequence of the set {‘ l is g ’, ‘ l is B ’} [0.25 pt] ? Why [0.25 pt ] ? (e) Is ‘ g is g ’ logically true, logically false, or contingent [0.25 pt] ? Why [0.25 pt] ? (f) Is the argument {‘ g is B ’, ‘ l is B ’}/‘ l is g ’ deductively valid or invalid [0.25 pt] ? Why [0.25 pt] ? (g) Is the set whose members are all the members of except for the sentence ‘ some B are not B ’ consistent [0.25 pt] ? Why [0.25 pt] ?

Solution

(b) Set is inconsistent because of the sentence \'some B are not B\'.

(c) No. Because starting from any one, the other one cannot be derived.

(d) Yes. Transitivity

(e) Logically true. Tautology.

(f) Deductively invalid. Causes contradiction if added in the set.

(g) Consistent. Every subset of it is consistent.