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I think (a) is correct. But, how about (b), (c) , (d)?

(a) John felt pity for the old man sitting under the tree.

(b) John felt the old man was very pity / pitiful.

(c) John was pity for the old man.

(d) John was sad for the pitiful old man.
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You're right, (a) is correct and the best of the four.
(b) 'pitiful' would work, but I would prefer 'thought' over 'felt'
(c) wrong
(d) 'felt' works better here
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Hi,
A small further comment.

'Pity' is a strong emotion.

We much more often say "I felt sorry for him'.

Clive