Cardinality of the set

Probability Level 3

Suppose $A$ is a set so that $A =$ { $a,b,c$ }. Which of the following is always true.

1.) The $|A|$ is always equal to 3.

2.) The $|A| \leq 3$

3.) The $|A| \geq 3$

3 only 1 and 2 only 1 only 2 and 3 only 2 only 1,2 and 3

1 solution

Paul Ryan Longhas
Feb 16, 2016

The always true is (2). If the element of A is distinct, then |A| = 3. But, if at least 2 elements of A are equal, then |A| = 2. Also, if three of them are equal, then |A| = 1. Thus, $|A| \leq 3$ .

Cardinality of the set

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