Which かたい is used incorrectly?
a. あの ひとは くちが かたい。
b. この えんぴつは かたい。
c. その もんだいは かたかった。
d. パンが かたくなった。
かたい is often remembered as “hard” so if I translate these 4 sentences with the word “hard”:
a. He has a hard mouth.
b. This pencil is hard.
c. That question was hard.
d. Bread became hard.
Looking at the English sentences above, you may pick a. as the odd one. However, かたい can mean “solid” or “firm” as well. “Hard” in c. means “difficult” so the odd one is c and it should read その もんだいは むずかしかった。
かたい can be written with 3 different kanji characters, 固い、硬い and 堅い.
固い is more like “solid” and it is most widely used among these three. Its opposite is ゆるい (loose).
硬い is more like “hard” and used to describe the state of things or attitude of people. Its opposite is やわらかい (soft or flexible).
堅い is more like “firm” and described the nature of people and/or things. Its opposite is もろい (fragile or brittle).
So if I rewrite the caption sentence using kanji:
a. あの人は口が堅い。He is tight-lipped.
b. この鉛筆は硬い。
d. パンが固くなった。(Some people may use 硬 but I think 固 is more common)