Set Notation and Language

List the elements of {x : x is a positive integer and $$2x+1\le12$$  }

(2 marks)

Write an example of set is empty set!

(1 mark)

Randy gives two sets to Andy, that are A = {a, e, i, o, u} and B = {l, m, n, o, p, q}. Andy said $$\left(A\cap B\right)'$$  = O

(1 mark)

Which of the following statements are true (T) and which are false(F)?

(i) $$7\notin\left\{2,3,6\right\}$$  

(ii) $$6\notin\left\{x:x\ is\ an\ even\ number\right\}$$  

(iii) $$If\ A\ =\ \left\{1,2,3,4\right\}\ and\ B=\left\{whole\ number\ less\ than\ 4\right\},\ then\ A\ =\ B$$  

(iv) $$2\in\left\{x:x\ is\ a\ prime\ number\right\}$$  

(v) $$15\notin\left\{\left(x:x\ is\ a\ prime\ number\right)\right\}$$  

(5 marks)

If $$\xi=\left\{1,2,3,4,5\right\}$$  , $$A=\left\{1,2,4\right\}$$  and $$B=\left\{1,4,5\right\}$$ , list the elements of the set $$\left(A\cup B\right)\cap\left(A\cup B\right)'$$  

(2 marks)

If $$\xi=\left\{integers\ \ from\ 1\ to\ 12\right\}$$  

P = {prime numbers}

Q = {odd numbers}

list of the elements of $$P'\cap Q'$$  

(3 marks)

Which venn diagram is represent $$\left(A\cap B\right)'$$  

(1 mark)

Shade the set represent $$A\cup\left(B\cap C\right)'$$  

(1 mark)

In a group of 60 people, 27 like cold drinks and 42 like hot drinks and each person likes at least one of the two drinks. How many like both coffee and tea?

In a school, all pupils play either Hockey or Football or both. 400 play Football, 150 play Hockey, and 130 play both the games. Find

(i) The number of pupils who play Football only,

(ii) The number of pupils who play Hockey only,

(iii) The total number of pupils in the school.

(4 marks)