Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit

PHIL1012 Introductory Logic          ·          Problem Set 4           ·         Week 6

1.  Consider a three-place connective ⊛ that has the following truth table:

Following the method explained in the textbook §6.6.2, pp.129–131, show that ⊛ is definable in terms of 一, Λ and V.

2.   (a)  Call a two-place connective self-negating if the proposition obtained by putting α in both the first and second place of that connective is equivalent to 一α . (That is, where . is some two-place connective, . is self-negating if (α . α) is equivalent to 一α .)

In §6.6.2 of the textbook (on p.128 in the print edition) all possible two-place connectives  are presented  in  a table.   Which  of  these  connectives  are  self- negating?   Your answer should give  all  the  self-negating ones and not give any of the ones that are not self-negating.  For each connective that you give, justify your claim that it is self-negating by giving appropriate truth tables.

(b) Is the following statement true or false? Justify your answer:

Any set containing conjunction,  disjunction,  and  one  self-negating two-place connective, is functionally complete.