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Question of the Day

Hello! I'd like to ask about syllogisms. I have a particular problem when understanding this certain syllogism: Some girls are single. Some girls are sad. Therefore, some girls are single and sad. While I think it is valid, I cannot fully make an accurate explanation as to why it is. Hoping somebody could help me. Thanks!

The syllogism in question is not valid. Nothing logically guarantees that the set of single girls and the set of sad girls overlap. Even if both sets have members, it does not follow that they have any members in common. Compare: Some polygons are squares. Some polygons are triangles. But it is false that some polygons are square triangles.