In this question are given four statements followed by five conclusions, one of which definitely does not logically follow (or is not a possibility of occurrence) from the given statements. That conclusion is your answer.

Note:- You have to take the four given statements to be true even if they seem to be at variance with commonly known facts and then decide which of the given conclusions logically does not follow from the given statements disregarding commonly known facts.

Statements:-
All references are mails.
All mentions are references.
All comments are mentions.
No mail is a declaration.

Conclusions:-
a. No reference is a declaration.
b. All comments are mails.
c. No mention is a declaration.
d. All declarations being comments is a possibility.
e. Atleast some mails are mentions.

No reference is a declaration

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All comments are mails

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No mention is a declaration

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All declarations being comments is a possibility

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Atleast some mails are mentions

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Solution

The correct option is D All declarations being comments is a possibility
All mentions are references (A) + All references are mails (A) = All mentions are mails (A) $\to$ conversion $\to$ Some mails are mentions (I). Hence, (e) follows.
Again, All comments are mentions (A) + All mentions are references (A) = A + A = All comments are referencees (A) + All references are mails (A) = A + A + A = All comments are mails. Hence, (b) follows.
Again, All references are mails (A) + No mail is a declaration (E) = A + E - E = No reference is a declaration (E). Hence, (a) follows.
Now, All comments are mails (A) + No mail is a declaration (E) = A + E = E = No comment is a declaration (E). Hence (d) does not follow.
Now, All mentions are mails (A) + No mail is a declaration (E) = A + E = E = No mention is a declaration (E). Hence, (c) follows.

So, only conclusion (d) does not follow

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