Describe all the sets and subsets 2/3 belongs to
The set containing 2/3 is the set {2/3}.
As for its subsets:
- The empty set {} is a subset of every set, including the set {2/3}.
- The set {2/3} itself is a subset of itself.
- Additionally, the power set of {2/3}, denoted by P({2/3}), is the set containing all possible subsets of {2/3}, which consists of two subsets: the empty set {} and the set {2/3}.
To determine all the sets and subsets that 2/3 belongs to, we need to analyze its inclusion in various mathematical sets. Here are the possibilities:
1. The set of Real Numbers (ℝ): 2/3 is a rational number, as it can be expressed as a quotient of two integers. Therefore, it belongs to the set of Real Numbers.
2. The set of Rational Numbers (ℚ): As mentioned above, 2/3 is a rational number, which is a subset of the Real Numbers. Thus, 2/3 belongs to the set of Rational Numbers.
3. The set of Integers (ℤ): Since 2/3 is not an integer (i.e., a whole number), it does not belong to the set of Integers.
4. The set of Natural Numbers (ℕ): Similarly, 2/3 is not a natural number (i.e., a positive whole number), so it does not belong to the set of Natural Numbers.
5. The set of Whole Numbers (ℤ⁺): Again, 2/3 does not meet the criterion of being a whole number, so it does not belong to the set of Whole Numbers.
6. The set of Irrational Numbers (ℝ - ℚ): Irrational numbers cannot be expressed as a fraction of two integers. Since 2/3 is a rational number, it does not belong to the set of Irrational Numbers.
To summarize, the sets and subsets that 2/3 belongs to are the set of Real Numbers (ℝ) and the set of Rational Numbers (ℚ).
To describe all the sets and subsets that 2/3 belongs to, we first need to understand the concept of sets and subsets.
A set is a collection of distinct elements. It can contain any type of object or elements, such as numbers, letters, or other sets. For example, a set of even numbers could be {2, 4, 6, 8, ...}.
A subset is a set that contains only elements from another set, called the parent set. In other words, every element in a subset must also be present in the parent set. For example, if we have a parent set of {1, 2, 3, 4}, some possible subsets are {1, 2}, {3, 4}, and {1, 4}, among others.
Now, let's determine the sets and subsets that 2/3 belongs to.
1. Set of Real Numbers: 2/3 is a real number, so it belongs to the set of real numbers. This set includes all rational and irrational numbers.
2. Set of Rational Numbers: Since 2/3 can be expressed as a fraction, it belongs to the set of rational numbers. Rational numbers are numbers that can be expressed as a ratio of two integers (with a non-zero denominator).
3. Set of Fractions: As 2/3 is a fraction itself, it belongs to the set of fractions. Fractions represent a part of a whole and can be written in the form a/b, where a and b are integers and b is not zero.
4. Subset of Positive Rational Numbers: Since 2/3 is a positive fraction, it is a subset of the positive rational numbers. This subset includes all positive fractions expressed in the form a/b, where both a and b are positive integers.
5. Subset of Proper Fractions: A proper fraction is a fraction where the numerator is smaller than the denominator. Since 2/3 is a proper fraction, it belongs to this subset.
These are some examples of sets and subsets that 2/3 belongs to. However, keep in mind that there are many more sets and subsets that 2/3 could be a part of depending on the context and specific mathematical definitions being used.