Sets 2
4 marks · HardLet .
Write the following sets using set-builder notation:
The set of all negative elements of .
The set of all in such that .
The set of elements of that are not odd numbers.
The set of all elements in such that .
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) { x \in S : x < 0 }
(b) { x \in S : x^2 < 5 }
(c) { x \in S : x \text{ is even} }
(d) { x \in S : |x| \leq 2 }
Common mistakes: Omitting to specify that x ∈ S; Incorrect inequality signs; Missing absolute value notation
Show mark scheme and worked solution
Marking points
B1 (a) · 1 mark · Correct set-builder notation for all negative elements of S.
B1 (b) · 1 mark · Correct set-builder notation for in with .
B1 (c) · 1 mark · Correct set-builder notation for elements not odd (i.e., even) in S.
B1 (d) · 1 mark · Correct set-builder notation for in such that .
Worked solution
a) The negative elements of S: x ∈ S, x < 0.
b) Elements with x^2 < 5: x ∈ S, x^2 < 5.
c) Elements not odd numbers—in S, these are the even numbers.
d) Elements with .