Sets 2
4 marks · HardConsider the set .
A student claims the set can also be written in the form .
Explain whether the student's claim is correct. Justify your answer, referring to set-builder notation.
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
Must show: States the actual square numbers in T, Explains whether the described sets are equal, Identifies the difference using set-builder notation
Common mistakes: Assuming the two notations describe the same set without checking elements; Not specifying the elements
Show mark scheme and worked solution
Marking points
M1 · 1 mark · Lists the square numbers in T (4 and 9).
M1 · 1 mark · Writes out the set defined by within T.
A1 · 1 mark · States clearly whether the sets are equal (they are not).
E1 · 1 mark · Valid explanation supporting the conclusion, referring to set-builder notation or elements.
Worked solution
The set within T is \{4, 9\} because these are the only numbers in T that are perfect squares.
The set within T means all natural numbers in T with 2 < x < 10, so that is \{3, 4, 5, 6, 7, 8, 9\}.
Therefore, the sets are not equal: \{4, 9\} is not the same as \{3, 4, 5, 6, 7, 8, 9\}.
The first set includes only the square numbers in T, while the second includes all numbers between 3 and 9 inclusive in T. The set-builder expressions describe different sets.