Determine whether the statement is true or false. if it is true, explain why it is true. if it is false, give an example to show why it is false. a proper subset of a set is itself a subset of the set but not necessarily vice versa.
true. let a={1,2,3} and b={1}. then b is a proper subset of a, and thus a subset of a. but a is not a proper subset of b.
true. let a={1,2} and b={2,3}. then b is a proper subset of a, and thus a subset of a. but a is not a proper subset of b.
false. let a={1,2,3} and b={1,2,3}. then b is a proper subset of a, and thus a subset of a, and a is a proper subset of b.
false. let a={1,2} and b={2,3}. then b is a proper subset of a, and thus a subset of a, and a is both a subset of a and a proper subset of a.
false. let a={1,2} and b=∅. then b is a proper subset of a, and thus a subset of a, and a is a subset of b, because everything is a subset of ∅.