Final answer:
In mathematics, '1 ∈ S' means the number one is a member of set S. In Java, 's.contains(1)' checks if the Set object 's' contains the number one. Both represent the same check for element membership but in different contexts.
Step-by-step explanation:
The student's question involves comparing mathematical set membership notation with Java programming language code. When it is said that 1 ∈ S, this means the integer 1 is a member of the set S in mathematical terms. In Java, the expression s.contains(1) checks if the object s, which is an instance of Java's Set interface, contains the integer 1. Both expressions serve the same purpose: to verify the presence of the element 1 in the set. The difference lies in context; one is used in mathematical set theory, while the other is in Java programming.
In the context of probability problems, set membership is important. For example, if T is the event of getting a white ball twice from a box with one white and one red ball, then a successful outcome such as getting a white ball twice would be an element of the set T. When implementing such scenarios in Java, the contains method can be used to ascertain if a particular outcome is part of the event set.
Overall, while the contexts are different, the core concept remains the same. The mathematical notation and Java method both check if an element is part of a set, a fundamental operation in both discrete mathematics and computer science.