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}

Question

Mathematics

Hanna Hensley

11 August, 02:35

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}

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Giuliana Acevedo · 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}