Definition: Conjunction
Let \(L\) be a set of propositions with the interpretation $I$ and the corresponding valuation function $[[]]_I$.
A conjunction "\(\wedge \)" is a Boolean function.
\[\wedge :=\begin{cases}L \times L & \mapsto L \\
(x,y) &\mapsto x \wedge y.
\end{cases}\]
defined by the following truth table:
Truth Table of the Conjunction
:
$[[x]]_I$ $[[y]]_I$ $[[x \wedge y]]_I$
\(1\) \(1\) \(1\)
\(0\) \(1\) \(0\)
\(1\) \(0\) \(0\)
\(0\) \(0\) \(0\)
We read the conjunction $x\wedge y$
“$x$ and $y$”.
Notes
 The conjunction of two propositions is only true if they are both true, otherwise it is false.
 The standard English conjunction is and. But there are some others, which are the same logically: but, however, although, though, even though, moreover, furthermore, and whereas, e.g.
 "I passed logic, and I did not pass calculus."
 "I passed logic, but I did not pass calculus."
 "I passed logic, however I did not pass calculus."
 "I passed logic, although I did not pass calculus."
 "I passed logic, though I did not pass calculus."
 etc.
Table of Contents
Corollaries: 1
 Proposition: Associativity of Conjunction
Mentioned in:
Branches: 1
Corollaries: 2 3
Definitions: 4 5 6 7 8 9 10
Examples: 11
Lemmas: 12 13 14 15 16
Parts: 17
Proofs: 18 19 20 21 22 23 24 25 26 27 28 29 30
Propositions: 31
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References
Bibliography
 Kohar, Richard: "Basic Discrete Mathematics, Logic, Set Theory & Probability", World Scientific, 2016