in Logical Reasoning
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Directions for questions: Answer the questions based on the following information. $A$ and $B$ are two sets (e.g. A = Mothers, B = Women). $C = A . B \implies$ The elements that could belong to both the sets (e.g. women who are mothers) is given by the set $C = A . B. D = A \cup B \implies$ The elements which could belong to either $A$ or $B$, or both, is indicated by the set $D = A \cup B. \phi \implies$ A set that does not contain any elements is known as a null set represented by $\phi$ (e.g. if none of the women in the set $B$ is a mother, then $C = A .B$ is a null set, or $C = \phi$ ).

Let 'V‘ signify the set of all vertebrates,

'M‘ the set of all mammals,

'D‘ dogs, 'F‘ fish 'A‘ alsatian and

'P‘, a dog named Pluto.


If $Y = F . (D . V)$ is not a null set, it implies that

  1. All fish are vertebrates 
  2. All dogs are vertebrates 
  3. Some fish are dogs 
  4. None of these 
in Logical Reasoning
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