If R is the set of real numbers and Q is the set of rational numbers, then what is R – Q?
R – Q is the set of irrational numbers, denoted by T. It consists of all real numbers that are not rational numbers. Examples include , , and π.
Explanation
The question asks about the set difference R – Q. According to the textbook context, the set of irrational numbers T is defined as T = {x : x ∈ R and x ∉ Q}, meaning all real numbers that are not rational. Since Q ⊂ R (rational numbers are a subset of real numbers), the difference R – Q gives us exactly those elements in R that are not in Q, which is the set of irrational numbers T. The context explicitly states that members of T include , and π.
Solution Steps
Step 1: Identify that R is the set of real numbers and Q is the set of rational numbers.
Step 2: Recall that Q ⊂ R (rational numbers are a subset of real numbers).
Step 3: Apply the definition of set difference: R – Q = {x : x ∈ R and x ∉ Q}.
Step 4: From the context, this set is defined as the set of irrational numbers T = {x : x ∈ R and x ∉ Q}.
Step 5: Conclude that R – Q = T, the set of irrational numbers.