The problem asks which of the given set membership statements are correct. A. $\frac{7}{3} \notin N$, where $N$ represents the set of natural numbers. B. $\frac{7}{5} \notin Z$, where $Z$ represents the set of integers. C. $\frac{9}{2} \in Q$, where $Q$ represents the set of rational numbers. This option is missing from the image but present in the original image. D. $\frac{2}{3} \notin R$, where $R$ represents the set of real numbers.

1. Problem Description

The problem asks which of the given set membership statements are correct.

A. $\frac{7}{3} \notin N$, where $N$ represents the set of natural numbers.

B. $\frac{7}{5} \notin Z$, where $Z$ represents the set of integers.

C. $\frac{9}{2} \in Q$, where $Q$ represents the set of rational numbers. This option is missing from the image but present in the original image.

D. $\frac{2}{3} \notin R$, where $R$ represents the set of real numbers.

2. Solution Steps

A. The set of natural numbers $N = \{1, 2, 3, ...\}$. Since $\frac{7}{3} = 2.333...$ is not a natural number, $\frac{7}{3} \notin N$ is correct.

B. The set of integers $Z = \{..., -2, -1, 0, 1, 2, ...\}$. Since $\frac{7}{5} = 1.4$ is not an integer, $\frac{7}{5} \notin Z$ is correct.

C. The set of rational numbers $Q$ is the set of numbers that can be expressed as a fraction $\frac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$. Since $\frac{9}{2}$ can be expressed as a fraction where both the numerator and the denominator are integers, $\frac{9}{2} \in Q$ is correct.

D. The set of real numbers $R$ includes all rational and irrational numbers. Since $\frac{2}{3}$ is a rational number, it is also a real number. Therefore, $\frac{2}{3} \in R$, and $\frac{2}{3} \notin R$ is incorrect.

3. Final Answer

A, B and C are correct.