Question

Determine whether each of these pairs of sets are equal.

a. {1,3,3,3,5,5,5,5},{5,3,1}

b. {{1}}{1,{1}}

c. ∅,{∅}

Answer 1

a. Since each element of the set {1,3,3,3,5,5,5,5} belongs to the set {5,3,1}, and each element of the set {5,3,1} belongs to the set {1,3,3,3,5,5,5,5}, we conclude that these sets are equal.

b. Since $1\notin\{\{1\}\},$ we conclude that these sets are not equal.

c. Since $\emptyset\notin\emptyset,$ we conclude that these sets are not equal.