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Cardinality

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Question

Find the cardinal number of the following sets.
(i) $A =$ { $x : x$ is a prime factor of 12 }
(ii) $B = {x : x \in W, x \leq 5}$

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Solution

(i) Factors of 12 are 1,2,3,4,6,12. So, the prime factors of 12 are 2,3.
We write the set A in roster form as $A = {2, 3}$ and hence $n (A) = 2$ .
(ii) $B = {x : x \in W, x \leq 5}$ . In Tabular form, $B = {0, 1, 2, 3, 4, 5}$ .
The set B has six elements and hence $n (B) = 6$

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