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State whether each of the following set ...

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 number 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).

Text Solution

AI Generated Solution

Let's analyze each of the sets given in the question step by step to determine whether they are finite or infinite. ### Solution: **(i) The set of lines which are parallel to the x-axis:** - In a Cartesian plane, we can draw an infinite number of lines parallel to the x-axis. Each line can be represented by the equation \(y = c\), where \(c\) can take any real number value. Since there are infinitely many real numbers, the set of lines parallel to the x-axis is an **infinite set**. **(ii) The set of letters in the English alphabet:** ...
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