We need to be a little careful here. If \(B\) contains 3 elements, then \(A\) contains just the number 3 (listed twice). So that would make \(|A| = 1\text{,}\) which would make \(B = \{1, 3\}\text{,}\) which only has 2 elements. Thus \(|B| \ne 3\text{.}\) This means that \(|A| = 2\text{,}\) so \(B\) contains at least the elements 1 and 2. Since \(\card{B} \ne 3\text{,}\) we must have \(\card{B} = 2\text{,}\) which agrees with the definition of \(B\text{.}\)
in-context