Math Problem Statement

Svara på 4b 5

Svara på 4b (5) från bilden

Solution

To solve question 4b (5), we need to evaluate the statement "{{1}} \subseteq A" for the set A={0,{1},,{2,3}}A = \{0, \{1\}, \emptyset, \{2,3\}\}.

Interpretation:

  • The statement is about whether the set {1}\{1\} (the set containing 1) is a subset of AA.
  • A subset means that every element in {1}\{1\} must also be an element in AA.

Check:

  • The set {1}\{1\} contains only one element, which is the number 1.
  • Looking at the set A={0,{1},,{2,3}}A = \{0, \{1\}, \emptyset, \{2,3\}\}, we see that {1}\{1\} itself is an element of AA, but 1 is not an element of AA.

Thus, the set {1}\{1\} is not a subset of AA, since 1 is not an element of AA.

Conclusion:

The statement in 4b (5), "{1}A\{1\} \subseteq A," is false.

Would you like further details on subsets or any related questions?

Related questions:

  1. What is the difference between a subset and an element of a set?
  2. Can an empty set be a subset of any set?
  3. Is the set {{1}}A\{\{1\}\} \subseteq A true for this example?
  4. How can we determine whether a set is a subset of another set in general?
  5. What happens if we change the set AA in this problem?

Tip:

When evaluating whether a set is a subset of another, remember that each element of the subset must also be an element in the main set.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Subsets
Elements of Sets

Formulas

-

Theorems

Definition of Subsets
Membership in Sets

Suitable Grade Level

Grades 9-12