Choose the variant where all occurrences of the letter 'Ы' are indicated.

Explanation:

The question asks to identify a word where the letter 'Ы' is correctly used, implying that it's the only letter missing in the provided words that should be 'Ы'. Let's examine the options:

• a) Доказ..вать: To form the word 'доказывать' (to prove), we need 'ы' after 'з'. So, доказывать.
• b) Досад..вать: To form the word 'досадовать' (to be annoyed), we need 'о' after 'д'. The letter 'ы' is not used here.
• c) Завид..вать: To form the word 'завидывать' (to envy), we need 'ы' after 'д'.

The question states "в котором указаны все случаи, пишется буква Ы?" (in which all cases are indicated, the letter 'Ы' is written?). This phrasing is a bit awkward. It likely means to find the option where 'Ы' should be inserted correctly.

Let's re-read: "Выберите вариант, в котором указаны все случаи, пишется буква Ы?" This means we need to find the option that *correctly inserts* 'Ы' in all the necessary places within that option.

Let's re-examine the words assuming 'Ы' is the missing letter:

• a) Доказ..вать -> Доказывать. Here, 'ы' is correctly placed after 'з'. This word fits the pattern of using 'ы' in verb suffixes after certain consonants.
• b) Досад..вать -> Досадовать. The verb is 'досадовать', which uses 'о', not 'ы'. If the blank was meant for 'о', then the option is irrelevant to finding 'ы'.
• c) Завид..вать -> Завидывать. Here, 'ы' is correctly placed after 'д'.

The question asks for the option where "all cases are indicated, the letter Ы is written?". This implies we are looking for the correct usage of 'Ы'.

If we look at the options as presenting words where 'Ы' needs to be inserted:

• a) Доказ..вать: Becomes доказывать. This is a correct usage of 'ы'.
• b) Досад..вать: Becomes досадовать. No 'ы' here.
• c) Завид..вать: Becomes завидывать. This is a correct usage of 'ы'.

The question is "Выберите вариант, в котором указаны все случаи, пишется буква Ы?" (Choose the variant in which all cases are indicated, the letter 'Ы' is written?). This wording suggests that the variant itself contains the correct spelling with 'Ы'.

Let's assume the question is asking which of these words correctly uses the letter 'Ы' as the missing letter.

Consider common rules for 'Ы' after consonants in verb suffixes:

After certain consonants (like г, к, х, ж, ш, ц, ч, щ) and in some other cases, verbs often have -ыва- or -ива- endings. However, here we are dealing with roots ending in consonants where 'ы' might appear.

Rule: In verbs ending in -ывать (like доказывать, завидывать), the 'ы' is part of the suffix.

Let's re-examine the words with the assumption that 'Ы' is the missing letter:

• a) Доказ..вать: If we insert 'ы', we get доказывать. This is a correct Russian word.
• b) Досад..вать: If we insert 'ы', we get 'досадывать'. This is not a standard Russian word. The correct verb is 'досадовать'.
• c) Завид..вать: If we insert 'ы', we get завидывать. This is a correct Russian word.

The question asks for the variant where "all cases are indicated, the letter Ы is written?". This phrasing is still problematic. It could mean: "Choose the variant where the letter 'Ы' is correctly used in all its occurrences within that variant." Or it could mean: "Choose the variant where the blank should be filled with 'Ы' to make it correct." Given the dots (..), the latter is more likely.

So, we are looking for the option where filling the blank with 'Ы' results in a correctly spelled word, and this should represent all such cases within that option.

Both 'доказывать' and 'завидывать' correctly use 'ы' in their suffixes.

However, the question asks for *the* variant, implying only one correct answer.

Let's consider the possibility that the question is testing a specific rule about 'Ы'.

There's a rule regarding verbs ending in -ивать/-ывать:

• If the present tense ends in -иваю, the infinitive ends in -ивать.
• If the present tense ends in -ываю, the infinitive ends in -ывать.

Let's check the present tense for these verbs:

• 'Доказывать': Я доказываю (ends in -ываю), so infinitive is доказывать. Correct.
• 'Завидывать': Я завидую (ends in -ю, from завидовать, which is an irregular verb. The infinitive form 'завидовать' uses 'о', but the related verb 'завидовать' often involves 'ы' in derivations or related forms. The verb 'завидовать' itself has 'о'. However, 'завидывать' is also a recognized verb form meaning to envy, although less common than 'завидовать'. Example: 'Завидывать ему стало.' A common alternative is 'завидовать', which has 'о' in the infinitive.)

Let's look at the common verb 'завидовать'. It is 'завидовать', not 'завидывать'. If the intention was 'завидовать', then putting 'ы' is wrong.

Let's re-evaluate based on typical Russian orthography rules:

• Доказывать: Correct. 'ы' after 'з'.
• Досадовать: Correct. 'о' after 'д'. No 'ы'.
• Завидовать: Correct. 'о' after 'д'. No 'ы'.

If the intended words are 'доказывать', 'досадовать', and 'завидовать', then only option 'a' correctly fills the blank with 'ы' to form 'доказывать'. Option 'c' would be 'завидовать' if the blank was for 'о'.

However, the presence of 'завид..вать' suggests that 'завидывать' might be the intended word, despite 'завидовать' being more common. If 'завидывать' is a valid word, then both 'a' and 'c' would be correct insertions of 'ы'. This contradicts the idea of a single correct option.

Let's look at the question again: "Выберите вариант, в котором указаны все случаи, пишется буква Ы?" It's asking for the variant where 'Ы' is written correctly in *all applicable cases*. This implies that if a variant has multiple blanks, all should be filled with 'Ы', or if there's only one blank, it should be 'Ы'.

If we assume the options are single words and we need to insert 'Ы':

a) Доказывать - Correct.

Both 'a' and 'c' use 'ы' correctly. This is still problematic.

Let's consider the possibility that the question is asking for a rule associated with 'Ы'. A common rule involves distinguishing between 'и' and 'ы' after roots.

Another possibility is that the question is testing the rule: "In Russian, after certain consonants (г, к, х, ж, ш, ц), 'и' changes to 'ы' in the infinitive and past tense if the preceding sound is a hard consonant, and if the root of the word has 'и'. However, 'ы' is generally written after 'ж', 'ш', 'ц', 'ч', 'щ' and after 'г', 'к', 'х' in roots when they are followed by 'а' or 'у'. In suffixes like -ывать, the 'ы' is retained.

Let's assume the question is testing the verb suffix -ывать/-ивать.

• Доказывать: Present tense 'доказываю'. Infinitive is -ывать. So, ы.
• Досадовать: No -ывать/-ивать ending.
• Завидывать: Present tense 'завидую'. The infinitive rule is tricky here. However, 'завидывать' is a recognized form.

Given that both 'a' and 'c' seem to correctly insert 'ы', and 'b' does not use 'ы', there might be a subtle distinction or a common error being tested.

Let's consider the common words and their spellings.

Доказывать is standard.

Завидовать is standard. The verb 'завидывать' exists but is less common and sometimes considered a variant or older form. If the question expects the most standard form, then 'завидовать' would be the target, meaning 'ы' would be incorrect for 'c'.

If 'завидовать' is the intended word for option (c), then inserting 'ы' would be an error. This would leave 'a' as the only correct option.

Let's assume this interpretation: The question asks to fill the blank with 'Ы' and form a correct word. Both 'a' and 'c' can form correct words using 'ы'. However, if 'завидовать' is considered the primary verb, then 'завидывать' is incorrect.

Let's go with the most common and unambiguous usage.

Доказывать is definitively correct with 'ы'.

Завидовать is definitively correct with 'о'. If 'завид..вать' is presented, it suggests an attempt to spell 'завидывать', which, while existing, is less standard than 'завидовать'.

Therefore, option 'a' is the most reliable correct answer.

Ответ: а) Доказ..вать (meaning доказывать)