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Abstract Algebra

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Binary Operations from Logic

ABSALG-VFMREJ

Let $S$ be the set of true-false statements and $p,q\in S$. Identify any of the following operations which is not a binary operation of $S$.

A

Logical negation (not): $p\mapsto \sim p$

B

Logical conjunction (and): $(p,q)\mapsto p\wedge q$

C

Logical disjunction (or): $(p,q)\mapsto p\vee q$

D

Tautology: $(p,q)\mapsto p\vee (\sim p)$

E

None of the above.