Write the following in set notation:

Question

Write the following in set notation:

(a) The set of all real numbers greater than 7 but less than 173.
(b) 𝑄d = 200 − 5𝑃
(c) 𝑄s = −100 + 10𝑃
(d) 𝐷 ⋂ 𝑆 using the previous demand and supply equations

Answer 1

(a) The set can be represented in set notation as:

{𝑥 | 7 < 𝑥 < 173}

Explanation: In this case, we use the interval notation to represent the set of real numbers between 7 and 173, excluding the endpoints. The symbol "|" represents "such that", and 𝑥 is the variable representing the real numbers within the specified range.

(b) The equation 𝑄d = 200 − 5𝑃 can be rewritten in set notation as:

𝑄d = {200 − 5𝑥 | 𝑥 ∈ 𝑅}

Explanation: The set 𝑄d represents the quantity demanded (𝑄d) and is a function of the price (𝑃). In set notation, we use the variable 𝑥 to represent the prices (which can be any real number), and 𝑥 ∈ 𝑅 means 𝑥 belongs to the set of all real numbers.

(c) The equation 𝑄s = −100 + 10𝑃 can be written in set notation as:

𝑄s = {−100 + 10𝑥 | 𝑥 ∈ 𝑅}

Explanation: The set 𝑄s represents the quantity supplied (𝑄s) and is also a function of the price (𝑃). Similar to the previous equation, 𝑥 represents the price variable, and 𝑥 ∈ 𝑅 means 𝑥 belongs to the set of all real numbers.

(d) The intersection of sets 𝐷 and 𝑆 can be expressed in set notation as:

𝐷 ⋂ 𝑆 = {𝑥 | 𝑥 ∈ 𝑅, 𝑥 ∈ 𝑄d, 𝑥 ∈ 𝑄s}

Explanation: When finding the intersection of sets 𝐷 and 𝑆, we look for values that satisfy all the given conditions. Here, 𝑥 represents the common elements between the sets 𝐷 and 𝑆. The notation 𝑥 ∈ 𝑅 implies that 𝑥 is a real number, while 𝑥 ∈ 𝑄d and 𝑥 ∈ 𝑄s indicate that 𝑥 belongs to both sets 𝑄d and 𝑄s.