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Can $f[g(x)]$ and $g[f(x)]$ be used to prove that a function is onto?

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#functions #relations
49
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Relations on Surjective Functions

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#functions #logic #relations #equivalence-relations
204
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how to find maximal chain and antichain of a given partial order

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#relations
20
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Let $R$ be a relation on a set $A$. Define $T(R)=R\cup R^{-1} \cup \{(x,x)\mid x \in A \}$. Show that $T(R)$ is reflexive and symmetric.

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#relations
111
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Identifying properties of relations

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#discrete-mathematics #elementary-set-theory #proof-explanation #relations #problem-solving
233
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What does "the partition of $\mathcal{P}(A)$ induced by $R$" mean?

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#discrete-mathematics #relations #equivalence-relations #set-partition
56
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inverse relation need not to be a function.

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#functions #relations #inverse-function
127
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Equivalence Relation question - $(a,b)S(c,d) \iff a-b=c-d$ such that $(a,b),(c,d) \in\ \mathbb{N}\times\mathbb{N}$

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#relations #equivalence-relations
103
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Question about relations and equivalence classes.

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#discrete-mathematics #solution-verification #relations #equivalence-relations
40
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Relations and quotient groups.

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#solution-verification #relations #equivalence-relations
74
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How to prove this question related to multi-times composite relation $\mathcal{R}^{n}$

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#discrete-mathematics #relations
52
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Proving a statement about equivalence relations.

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#solution-verification #relations #equivalence-relations
42
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Question about equivalent classes.

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#solution-verification #recurrence-relations #relations #equivalence-relations
74
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Proof regarding quotient sets and functions.

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#solution-verification #relations #equivalence-relations #injective-module
71
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Solution verification about equivalence classes.

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#solution-verification #relations #equivalence-relations

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