Set Theory

The correct option is(D)

Concept: Countability of sets
A set is called:

• Countable if its elements can be put in one-to-one correspondence with
• Uncountable if this is not possible

Step 1: Form of rational numbers
Every rational number can be written as:
Step 2: Arrangement idea
We can arrange all such fractions in a grid and traverse them diagonally (Cantor’s method), ensuring every rational number is listed.
Step 3: Conclusion
Since all rational numbers can be listed in a sequence: