Master subsets of real numbers as intervals for CBSE Class 11 Applied Mathematics. Learn open, closed, and semi-open interval notation with solved examples.
An open interval (a, b) consists of all real numbers x such that a < x < b. The endpoints a and b are not included in the set. This is represented on a number line with hollow circles at a and b.
Step 1: Identify the bounds, a=2 and b=5.
Step 2: The set includes all numbers strictly between 2 and 5.
Step 3: Any number like 3.5 or 4.9 is in the set, but 2 and 5 are excluded.
Answer: {x : x ∈ ℝ, 2 < x < 5}
A closed interval [a, b] consists of all real numbers x such that a ≤ x ≤ b. The endpoints a and b are included in the set. This is represented on a number line with solid circles at a and b.
Step 1: Identify the lower bound -1 and upper bound 4.
Step 2: Since the inequality is ≤, both endpoints are included.
Step 3: Use square brackets to denote inclusion.
Answer: [-1, 4]
Semi-open or semi-closed intervals include one endpoint but not the other. The notation [a, b) means a ≤ x < b, while (a, b] means a < x ≤ b. These are essential for defining ranges where one boundary is inclusive.
Step 1: The lower bound 0 is excluded, so use a parenthesis.
Step 2: The upper bound 7 is included, so use a square bracket.
Step 3: Combine as (0, 7].
Answer: (0, 7]