\[\begin{align} 5 \times 8 &\text{ is larger than } (5-1)\times(8 + 1) \\ 7 \times 12 &\text{ is larger than } (7-1)\times(12 + 1) \\ 10 \times 17 &\text{ is larger than } (10-1)\times(17 + 1) \end{align} \]

Is it true that for all positive integers \(A\) and \(B\) \((\)with \(A<B),\) the value of \(A\times B \) **must** be larger than \((A-1)\times(B+1)?\)

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