Indicate which alcohol in each pair will undergo an elimination reaction more rapidly when heated with H$2$SO$4$

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Part A

There is a ring with six vertices, with alternating single and double bonds. A CH$2$OH group is attached to the first vertex.

There is a ring with six vertices, with alternating single and double bonds. A CH$2$CH$2$OH group is attached to the first vertex.

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Part B

There is a ring with six vertices, with an OH group attached to the first vertex.

There is a ring with six vertices, with an OH group attached to the first vertex. There is a double bond between the second $($clockwise$)$ and the third vertices.