PHIL1012 Introductory Logic · Problem Set 4 · Week 6
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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.
2023-09-06