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Let $A$ be a matrix with $m$ rows and $n$ columns. $a_{ij}$ denotes the real number in the cell in row $i$ and column $j$. How can I express (with a quantified statement) that:

  • All diagonal elements of $A$ are equal to $0$.
  • The largest value in the first row of $A$ is equal to $7$.

My answers:

  • $\forall i \forall j [i =j \to a_{ij}=0]$
  • $\exists j[a_{1j}=7] \land\forall j[a_{1j} \leq7]$

I would like to know if my answers are correct.

Tortar
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FPSX V
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  • Personally, I would add parenthesis to avoid parsing errors on the part of people; but I have been traumatized by "bad" parsers. In my experience, for elementary classes I would ditch the "->" in favour of and's/or's/not's. Of course in the "real" world "->" is fine. – rrogers Oct 27 '20 at 21:41

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