Question

5. Determine whether each of these pairs of sets are equal.

a) {1, 3, 3, 3, 5, 5, 5, 5, 5},{5, 3, 1} b) {{1}},{1,{1}} c) ∅,{∅}

6. Suppose that A = {2, 4, 6}, B = {2, 6}, C = {4, 6}, and D = {4, 6, 8}. Determine which of these sets are

subsets of which other of these sets.​

Answer 1

Answer:

5. Determine whether each of these pairs of sets is equal.

a) {1, 3, 3, 3, 5, 5, 5, 5, 5}, {5, 3, 1}

• The two sets are equal.
• We need to look only at the distinct elements, not the repetitions or the order. The two sets contain common elements 1, 3, and 5.
• Hence, they are equal.

b) {{1}}, {1, {1}}

• If the two sets are equal then the cardinality of the sets is the same.
• But, |{{1}}|=1 and |{1, {1}}|=2
• So, {{1}} and {1, {1}} are not same.

c) ∅,{∅}

• The cardinality of the two sets is not the same.
• |∅| = 0 but |{∅}| = 1
• So, ∅ and {∅} are not the same.

6. Determine which of these sets are subsets of which other sets.

The given sets are A = {2, 4, 6}, B = {2, 6}, C = {4, 6}, and D = {4, 6, 8}

• Each of the given sets is a subset of itself.
• The set B is a subset of set A as all the elements of B are present is A.
• The set C is a subset of set D as all the elements of C are present in D.

Therefore, set A is a subset of itself, set B is a subset of itself and set A, set C is a subset of itself and set D, and set D is a subset of itself.

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Answer 2

Answer:

The answer to the given question is-

a) {1, 3, 3, 3, 5, 5, 5, 5, 5},{5, 3, 1} - These two sets are equal.

b) {{1}},{1,{1}} - They are not equal.

c) ∅,{∅} - They are not equal.

• In the given sets,  A = {2, 4, 6}, B = {2, 6}, C = {4, 6}, and D = {4, 6, 8}.
• Set A is a subset of itself.
• Set B is a subset of itself and also a subset of set A.
• Set C is a subset of itself and also a subset of set D.
• Set D is a subset of itself.

Step-by-step explanation:

a) {1, 3, 3, 3, 5, 5, 5, 5, 5},{5, 3, 1}

The number of distinct elements without any repetition is the same in both sets. So they are equal.

b) {{1}},{1,{1}}

The number of elements is not the same in both sets. The first one has 1 element while the second one has 2 elements. So they are not equal.

c) ∅,{∅}

The number of elements is not the same in both sets. The first one has 0 elements while the second one has 1 element. So they are not equal.

• Given sets,

A = {2, 4, 6}, B = {2, 6}, C = {4, 6}, and D = {4, 6, 8}.

• Every set is a subset of itself.
• All the elements of set B are present in set A, so set B is a subset of set A.
• All the elements of set C are present in set D, so set C is a subset of set D.

Learn more about sets and subsets by clicking on the links given below-

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