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[esercizio] Dimostrare le seguenti affermazioni:

1. $A,B,C \in \mathcal{A}\;\;\stackrel{\displaystyle{\longrightarrow}}{AB}=\stackrel{\displaystyle{\longrightarrow}}{AC}\;\Rightarrow\;B=C.$


2. $\forall \mathbf{v} \in \mathbf{V}\;\;,\;\; \forall Q \in \mathcal{A}\;\;\;\; \e... ...\mathcal{A}\;\;:\;\; \stackrel{\displaystyle{\longrightarrow}}{PQ}= \mathbf{v}.$


3. $R,S,T \in \mathcal{A}\;\;\stackrel{\displaystyle{\longrightarrow}}{RS}=\stackrel{\displaystyle{\longrightarrow}}{TS}\;\Rightarrow\;R=T.$


4. $M,N \in \mathcal{A}\;\;\stackrel{\displaystyle{\longrightarrow}}{MN}=\mathbf{0}_{\mathbf{V}}\;\Rightarrow\;M=N.$