Question

Sort the given sets in the increasing order of their cardinalities(set with least cardinality at the bottom).

• A. Prime numbers<11
• B. Factors of 4
• C. Even numbers< 6
• D. {0}
• E. Δs with 2 sides

Answer 1

There is no triangle with 2 sides.
Thus, if $A$=Set of triangles with 2 sides, then the cardinality of A is 0.
Now, if $B$={0}, then $B$ has just one element(namely 0). Thus, the cardinality of $B$ is 1.
If $C$=Set of even numbers less than 6, then $C$={2,4} and thus, the cardinality of $C$ is 2.
Let $D$=Set of factors of 4. Then, $D$={1,2,4} and thus the cardinality of $D$ is 3.
And finally, if $E$=Set of prime numbers less than 11, then $E$={2,3,5,7} and thus the cardinality of $E$ is 4.
Now since $0<1<2<3<4$, we have the given order.