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Identify the type of set $N = \left\{ {x:x \in N,x \prec 7} \right\}$
  {\text{A}}{\text{. Finite Set}} \\
  {\text{B}}{\text{. Null Set}} \\
  {\text{C}}{\text{. Infinite Set}} \\
  {\text{D}}{\text{. Singleton Set}} \\

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Hint: In this question we need to find what type of set, N would be. In order to solve it we would find the possible values of x and then infer from them the nature of the set.

Complete step-by-step answer:
We have been given that $N = \left\{ {x:x \in N,x \prec 7} \right\}$

So, x belongs to natural numbers and x<7.

Therefore, x = {1,2,3,4,5,6,7}

So, as we can see that there are fixed counts of numbers in the set, hence N is a Finite Set.
So, option A. is correct.

Note: Whenever we face such types of problems the crux point to remember is that we need to have a good grasp over the concept of sets and its types. In these types of questions, we should always take the range in consideration and then apply the constraints that get us on the right track to reach the answer.
Last updated date: 29th Sep 2023
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