Question

What does it indicate when the cardinality of set S is less than or equal to the cardinality of set T?

a) |S| is strictly greater than |T|
b) |S| is equivalent to |T|
c) |S| is less than |T|
d) |S| is not comparable to |T|

Answer 1

c) |S| is less than |T|

Answer 2

The statement |S| ≤ |T| indicates that set S has a cardinality that is less than or equal to set T, meaning option (c) |S| is less than |T| is correct.

Step-by-step explanation:

When the cardinality of set S is less than or equal to the cardinality of set T, it indicates that the number of elements in set S is either less than or equal to the number of elements in set T. The cardinality, denoted by the vertical bars around the set (e.g., |S|), represents the count of distinct elements in the set. If we say that |S| ≤ |T|, it means that there are no more elements in set S than there are in set T. Therefore, the correct answer would be:

• c) |S| is less than |T|

This does not necessarily mean that sets S and T have an equivalent number of elements, only that set S does not have more elements than set T.