State True or False for the statements. \( \mathrm{P} \) \( \left|\...

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State True or False for the statements.
\( \mathrm{P} \) \( \left|\begin{array}{lll}x+1 & x+2 & x+a \\ x+2 & x+3 & x+b \\ x+3 & x+4 & x+c\end{array}\right|=0 \), where \( a, b, c \) are in A.P.

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