# Omega

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# 122 Posts

 Nov7 asked Determining equivalence classes of certain pairs for the relation $(a,b)R(c,d) \iff a^2 + 7b^2 = c^2 +7d^2$ Nov7 asked Finding order properties in the relation $aSb \iff \exists k \in \mathbb{N} : b = ak$ Nov7 asked Determining the properties for the relation over $P(\mathbb{N})$ where $ARB \iff A \cup B \in H$ Nov7 asked What is the equivalence class of a relation's element? Nov7 asked Finding the first, last, minimal and maximal elements in these relations. Nov6 asked Is my transitivity proof correct for the relation over $\mathbb{Z} \times \mathbb{Z}$ where $(a,b)R(c,d) \iff (a \le c \lor b \le d)$? Nov6 asked How can I determine that a relation lacks a property without using a counterexample? Nov5 asked Properties of relation $R$ on $\mathbb{N} \times \mathbb{N}:\;(a,b)R(c,d) \iff a -c = b -d$ Nov5 asked Is this equation to prove that $aRb \iff a^2 - b^2 = 1$ is antisymmetric correct? Nov5 asked Proving that the relation $a \le b \iff b - a \ge 0$ is antisymmetric and total. Nov4 asked Proving a relation's inverse's properties by knowing the original's. Nov4 asked How can I further simplify $(a \le b) \lor (b \le a)$ to prove that it is a tautology? Nov3 asked Proving that $aRb \iff a = b \lor a = b^2$ is antisymmetric. Nov3 asked Proving that $R$ is antisymmetric if and only if $G \cap G^{-1} \subseteq D$ Nov3 asked In a boolean matrix, what does the $n$ in $M_{R^n}$ represent? Sep29 asked Determining the truth value of certain quantifiers based on this proposition being false. Sep29 asked Determining $A \triangle B = B - C \implies A \subseteq B$ Sep28 asked How do I determine cardinalities, given the cardinality of other sets? Sep28 asked Determining $(X \cap Y \subseteq \overline{A} \land Y \subseteq B) \implies Y \subseteq B - A$ Sep27 asked How should I interpret a “but” when symbolizing logic statements?