Exercise I(a)

Introductory Chapter : Mathematical Logic, Proof and Sets12

Exercise I(a)1. Determine the elements of the following sets:

(a)

(b)

(c)

(d)

(e)

(f)

2. Determine the elements of the following sets:

(a)

(b)

(c)

(d)

(e)

(f)

3. Write the following statements in set notation:(a) The set of negative real numbers.(b) The set of positive integers.

(c) The set of real numbers between 0 and 2 excluding 0 and 2.(d) The set of rational numbers less than 1.

(e) The set of natural numbers which are multiples of 10.

Consider the following Venn diagram for questions 4 to 7:Fig 124. Shade in the following regions.(a)

(b)

(c)

(d)

5. Shade the following regions of the Venn diagram of Fig 12:(a)

(b)

(c)

(d)

6. Show that for the sets in Fig 12 we have the result .7. By shading the Venn diagrams of Fig 12 show that

8. Let be the universal set and , . Determine the members of the following sets:(a)

(b)

(c)

(d)

(e)

(f)

9. Let and . Determine the elements of the following sets:

(a)

(b)

(c)

(d)

(e)

(f)

(g)

For the remaining questions use the Venn diagram of Fig 13.

Fig 13

10. Shade in the following sets:

(a)

(b)

What do you notice about your results?11. Shade in the following sets:

(a)

(b)

What do you notice about your results?Brief Solutions to Exercise I(a)

1. (a)

(b)

(c)

(d)

(e)

(f)

2. (a)

(b)

(c)

(d)

(e)

(f)

3. (a)

(b) or

(c)

(d)

(e)

8. (a)

(b)

(c)

(d)

(e)

(f)

9. (a)

(b)

(c)

(d)

(e)

(f)

(g)

10. The same regions are shaded therefore .

11. Different sets, that is [Not Equal].

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