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# Logic0930 - Relationships between Ug Connectives 1 2 3...

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@ – ° ”± ±±± ±± Relationships between Connectives 1. Joint denial, Sheffer stroke 2. Binary connectives 3. Relationships between connectives

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Errata on p.76 Problem 10.15 => 16 “definable from ± and =/>” ± “ and =/ >” Reading for the next week Ch.11
HW #4 due Oct. 7th in class (will be posted on the web board) 1. Define , => from ↓ alone. Also, define v, => from | alone. (find the simplest forms) 2. Is definable from =>? Is v definable from =/>? Either case, justify your an- swers. Hint: examine and compare truth tables for these connectives.

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J : joint denial (NOR) ↓ p↓q: p and q are both false. p↓q ° ~(pvq), which explains the altern- ative name, NOR (not or). p q p↓q T T F T F F F T F F F T
10.10 ~, v, , => all definable from ↓ alone. Hint: once we define ~ and one of (v, , =>), the other connectives are all defin- able. ~p „ p↓p pvq ± ~(p↓q) ± (p↓q)↓(p↓q). If an island satisfies J , then it is a Boolean island.

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Logic0930 - Relationships between Ug Connectives 1 2 3...

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