Question

Let the set S = {1, {2}, 3, 4}. Which of the following is true?

a. {2} ∈ S
b. {1, 2} ⊆ S
c. {4} ∈ S
d. Ø ∈ S
e. {3, 4} ∈ S

Answer 1

In the given set S, certain statements are true or false. This answer provides a step-by-step explanation of each statement.

Step-by-step explanation:

The set S = {1, {2}, 3, 4}. Let's analyze each statement:

a. {2} ∈ S: The set S contains the element {2}, so this statement is true.

b. {1, 2} ⊆ S: The set S does not contain the element {1, 2}, so this statement is false.

c. {4} ∈ S: The set S contains the element {4}, so this statement is true.

d. Ø ∈ S: The symbol Ø represents an empty set. Since the set S contains elements, it is not empty. Therefore, this statement is false.

e. {3, 4} ∈ S: The set S contains the elements 3 and 4, so this statement is true.