query: Consequence of definition of Boolean algebra
positive_passages.docid: 22115
positive_passages.text: Equivalent definitions of Boolean Algebras
negative_passages.docid: 153440
negative_passages.text: Is logical implication always determinable from just the given statements?
negative_passages.docid: 100844
negative_passages.text: How should I understand "$A$ unless $B$"?
negative_passages.docid: 93342
negative_passages.text: Show that $\neg$ and $\wedge$ form a functionally complete collection of logical operators.
negative_passages.docid: 62172
negative_passages.text: Why does $-b < a < b \iff |a| < b$?
negative_passages.docid: 77957
negative_passages.text: How is $\mathbb N$ actually defined?
negative_passages.docid: 34913
negative_passages.text: Why does basic algebra provide one value for $x$ when there should be two?
negative_passages.docid: 145128
negative_passages.text: Understanding of Material Implication
negative_passages.docid: 42590
negative_passages.text: Understanding implication in logic truth tables (excerpt from textbook)
negative_passages.docid: 132837
negative_passages.text: Show that any monotone boolean function can be realize by the following connectives.
negative_passages.docid: 578
negative_passages.text: In classical logic, why is $(p\Rightarrow q)$ True if both $p$ and $q$ are False?
negative_passages.docid: 65536
negative_passages.text: Finitely generated ideals in a Boolean ring are principal, why?
negative_passages.docid: 65379
negative_passages.text: Deriving $\neg R$ from $\{R↔(R∨(P∧¬P)), R↔¬P, ¬P→(P↔(Q→Q)), P→Q\}$
negative_passages.docid: 144211
negative_passages.text: a second course in abstract algebra
negative_passages.docid: 77044
negative_passages.text: Boolean vs boolean in Java
negative_passages.docid: 20346
negative_passages.text: 'Algebraic' way to prove the boolean identity $a + \overline{a}*b = a + b$
negative_passages.docid: 93474
negative_passages.text: A Finite Boolean Ring is Generated by Finitely Many Copies of $\mathbb{Z} / 2 \mathbb{Z}$