NIMCET 2020 — Reasoning PYQ

Step 1: Simplify the statements by removing double negatives

Let's decode the two premises provided in the problem using basic set theory logic:

1. Premise 1: "There are no dancers that aren't slim"

   • This means that it is impossible to be a dancer without being slim.

   • In simpler terms: All dancers are slim.

   • Mathematically, if $D$ is the set of dancers and $S$ is the set of slim people:

     $$D\subseteq S$$

2. Premise 2: "No singers that aren't dancers"

   • This means that it is impossible to be a singer without also being a dancer.

   • In simpler terms: All singers are dancers.

   • Mathematically, if $I$ is the set of singers:

     $$I\subseteq D$$

Step 2: Combine the logical relationships

Now, let's link the two inclusion relationships together:

$$I\subseteq D\subseteq S$$

This tells us that the set of Singers is entirely contained inside the set of Dancers, which in turn is entirely contained inside the set of Slim people.

From this visual or mathematical nesting, we can directly conclude:

$$\text{All singers are slim. }(I\subseteq S)$$

Step 3: Evaluate the options

• A) There is not one slim person that isn't a dancer: This translates to "All slim people are dancers" ($S\subseteq D$). This is incorrect because the outer set can be larger than the inner set.

• B) All singers are slim: This matches our derived conclusion ($I\subseteq S$) perfectly.

• C) Anybody slim is also a singer: This translates to "All slim people are singers" ($S\subseteq I$), which is incorrect.

Correct Option: B