Question

What will be the set of the interval (a, b]?

(a) {x: a < x < b}

(b) {x: a ≤ x ≤ b}

(c) {x: a < x ≤ b}

(d) {x: a ≤ x < b}

I got this question in semester exam.

Origin of the question is Sets and their Representations in division Sets of Mathematics – Class 11

Answer 1

Correct choice is (c) {x: a < x ≤ b}

To explain I would say: The symbol ( ) implies that the value will always be less than or greater than the x value i.e. end points are not included.

{ } implies that all the values that does not satisfy a given interval are included inside {}.

[ ] implies that the value will always be less than equal to or greater than equal to the x value i.e. end points are included. This is possible only when both a and b are finite.