Let's start by determining the set \( A \). The set \( A \) is defined as:
\[ A = {x \mid x \in \mathbb{N}, x^2 = 4} \]
Here, \( \mathbb{N} \) denotes the set of natural numbers. The natural numbers are typically taken to start from 1, so we'll evaluate \( x^2 = 4 \):
The solutions to \( x^2 = 4 \) are \( x = 2 \) and \( x = -2 \). However, only \( x = 2 \) is a natural number. Therefore, we have:
\[ A = {2} \]
Now, let's evaluate the options provided:
(A) \( 4 \in A \) — This is false because \( A = {2} \) and does not contain 4.
(B) \( -26 \in A \) — This is also false for the same reason; \( A \) contains only the natural number 2.
(C) \( 2 \in A \) — This is true since \( 2 \) is indeed an element of \( A \).
(D) \( 2 \in A \) — This is also true, which appears to repeat option C.
From the analysis, the correct option is:
- (C) \( 2 \in A \)
- (D) \( 2 \in A \)
Both options C and D are correct statements regarding the set \( A \).