From 'All cats are animals' and 'Some animals are pets', we can only conclude that it's possible some cats are pets, but not definite.

Since no flower is a fruit, and all fruits are sweet, flowers cannot be sweet through this relation.

By transitive property: All doctors are professionals, and all professionals are educated, therefore all doctors are educated.

Some books are novels, and all novels are stories, therefore some books must be stories by logical deduction.

Since all trees are plants and no animal is a plant, logically no animal can be a tree.

From two 'some' statements, we cannot draw a definite conclusion about the relationship between singers and actors.

Although all gold is precious, only some precious things are expensive, so we cannot definitively conclude gold is expensive.

Since no criminal is honest, it means all criminals must be dishonest (contrapositive of the first statement).

Since some decision makers are not politicians, and all leaders are decision makers, some leaders must not be politicians.

While no student is lazy, and lazy people are unsuccessful, this doesn't tell us about unsuccessful students who might be lazy or for other reasons.