Answer

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**Hint:**Observing the sets carefully, we get to know that, \[N\] is a set of all natural numbers, and \[A\] is a set containing all the prime numbers and all the multiples of all prime numbers which implies that the set \[A\] contains all the natural numbers except \[1\]. And now, if we subtract set \[A\] from set \[N\],

We get only one element left in the resulting set i.e. \[1\]

**Complete step by step answer:**

Given, \[N\]represents the set of natural numbers, and

\[P\] denotes the set of Prime integers in\[N\].

\[A = \left\{ {n:n} \right. \in N,\]\[n\]is a multiple of some prime \[\left. {p \in P} \right\},\]

\[N - A = \left\{ {n \in N,n \notin \left. A \right\}} \right.\]

Now,

\[N\]denotes the set of natural numbers

\[ \Rightarrow N = \left\{ {1,2,3,4,5,6,7,...} \right\}\]

\[A = \left\{ {n:n} \right. \in N,\]\[n\] is a multiple of some prime \[\left. {p \in P} \right\}\]

\[ \Rightarrow A = \left\{ {n:n \in N,n = kp,p \in P,k \in N} \right\}\],

\[ \Rightarrow A = \left\{ {2,3,4,5,6,7,.......} \right\}\]

\[N - A = \left\{ {n \in N,n \notin \left. A \right\}} \right.\]

Hence,\[N - A = \left\{ 1 \right\}\], which is a singleton set.

**So, the correct answer is “Option D”.**

**Note:**A set is called an Empty set if it does not contain any element. It is denoted by \[\left\{ {} \right\}\] or \[\phi \].

A set of cardinality 2 means a set having two elements such as \[A = \left\{ {a,b} \right\}\]is a set having cardinality 2.

A finite set having cardinality greater than 2 means a set which has a definite number of elements but more than two elements such as \[A = \]{North, West, South, East} .

If a set \[A\] has only one element, then set \[A\] is called a singleton set. Like \[\left\{ a \right\}\] is a singleton set.

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