State whether each of the following set is finite or infinite:(i) The set of lines which are parallel to the x–axis(ii) The set of letters in the English alphabet(iii) The set of numbers which are multiple of 5(iv) The set of animals living on the earth(v) The set of circles passing through the origin (0, 0)

Explanation

To determine whether each of the following sets is finite or infinite, we will analyze each set one by one.

**(i) The set of lines which are parallel to the x-axis:**

1. **Understanding the set:** Lines parallel to the x-axis can be represented by the equation \(y = c\), where \(c\) is any constant value.
2. **Analysis:** Since \(c\) can take any real number value, there are infinitely many lines that can be drawn parallel to the x-axis.
3. **Conclusion:** Therefore, this set is an **infinite set**.

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