GO Classes DPP | Set theory | Set Operations | Stanford

Answer 1

Option A: True. $\mathbb{N} \in\{\mathbb{N}, \mathbb{R}\}$ because $\mathbb{N}$ is an element in the set.
Option B: False. $\mathbb{N}$ is not a subset of $\{\mathbb{N}, \mathbb{R}\}$; its elements (like $1,2,3 \ldots$ ) are not in the set.
Option C: False. $\mathbb{N} \in\{\mathbb{N}, \mathbb{R}\}$, so it is incorrect to say $\mathbb{N} \notin\{\mathbb{N}, R\}$.
Option D: True. $\mathbb{N} \nsubseteq\{\mathbb{N}, \mathbb{R}\}$ is correct because its individual elements are not all contained in the set.

Answer 2

Let  S = {N,R}

The thing to note here is that S has only two elements i.e N and R which are sets... dont confuse that all elements of N and R are in set S.

hence option A  and D are true

Answer 3

A, D

Answer 4

A D