If no actors can sing and all singers are artists, which of the following statements must be true?*No artists can sing.Some singers are not actors.All actors are singers.Some artists can act.
Question
If no actors can sing and all singers are artists, which of the following statements must be true?*No artists can sing.Some singers are not actors.All actors are singers.Some artists can act.
Solution
The statement that must be true is: "Some singers are not actors."
Here's the step-by-step reasoning:
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The first premise states that "no actors can sing." This means that there is no overlap between the group of actors and the group of singers.
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The second premise states that "all singers are artists." This means that the group of singers is a subset of the group of artists.
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Given these two premises, we can infer that while some artists may be singers, these artists cannot be actors (because no actors can sing).
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Therefore, the statement "Some singers are not actors" must be true, because all singers are artists, but no actors can sing.
The other statements are not necessarily true based on the given premises. For example, we don't know whether some artists can act or not, because the premises don't provide information about this. Similarly, we can't infer that "no artists can sing" or "all actors are singers" from the given premises.
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