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

1 answer

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 \( A \).