# sets, question 1, grade 10

20/06/2016

1)

Given the set E={a,4,5,6,7,8,b,10,11,12,13,c}

A) The elements of the set E represent the scores of 12 students in a math quiz (out 0f 15), arranged in the increasing order.

1) Knowing that the range is 11 and the mean is 8.5, calculate a,b, &c.

2)Find the % of students who failed.

B) In what follows , suppose that (a=3, b=9, and c=14)

Given the following subsets of E:

• A={ x $\in$ N/x is a solution of the equation $\left|{3x - 6}\right|=\left|{x - 6}\right|$ }
• B={x $\in$ E/x is a divisor of 14}
• C={x $\in$ E/ $\left|{2x-9}\right|\leqslant7$ }
• D={4,6,8,10}
• 1) Write A,B,and C in Roster's Notation.
• 2) Write D in Set Builder Notation.
• 3) Show that: $\overline {\overline C \cap \overline D } = C \cup D$