Question

For the following pairs of sets, state which of these statements is true: "A is a subset of B", "B is a subset of A", "A is a proper subset of B", "B is a proper subset of A". It’s possible for multiple statements to be true, or none of them. a. A = {3, +√5 2 − 4 2, √27 3 }, B = {3,{3},{3}} b. A = {{1, 2},{2, 3}},B = {{1, 2, 3}} c. A = {1, 2, 3},B = {{1},{2},{3}} d. A = {√16,{4}} , B = {4}

Answer 1

a. A = {3, +√5 2 − 4 2, √27 3 }, B = {3,{3},{3}} (None of them)

as there are no elements of either sets, those are completely present in other set.

b. A = {{1, 2},{2, 3}},B = {{1, 2, 3}} (None of them)

as there are no elements of either sets, those are completely present in other set.

c. A = {1, 2, 3},B = {{1},{2},{3}} (None of them)

as there are no elements of either sets, those are completely present in other set.

d. A = {√16,{4}} , B = {4} (B is a proper subset of A)

All elements of B i.e. 4 is present in set A with an additional element also there in A i.e. {4}