Question

If A = \{x / x \in N, x ^ 2 = 4\} then which of these is correct:(A) * 4 \in AB)-26 A(C) 2 EA(D)2 € A

Answer 1

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 \( A \).