Question

A. List the members of the following sets

1. {x| x is real numbers and x2 = 1}

2. {x| x is an integer and -4 < x ≤ 3}

B. Use set builder notation to give description of each of these sets.

1. {a, e,i ,o, u}

2. {=2, -1, 0, 1, 2}

C. Let A= (a, b, c), B = (x, y) and C = (0, 1)

Find:

1. A U C

2. C x B

3. B – A

4. (A ∩ C) U B

Answer 1

A.

1. If ${x^2} = 1$ then $x = \pm 1$ . So  {x| x is real numbers and x2 = 1}= {-1, 1}
2. {x| x is an integer and -4 < x ≤ 3}={-3, -2, -1, 0, 1, 2, 3}

B.

1. {a, e,i ,o, u}= {x| x is vowel of the english alphabet}
2. {-2, -1, 0, 1, 2}={x| x is an integer and -2≤ x ≤ 2}

С. let's find

1. $A \cup C = \{ x|x \in A \vee x \in C\} = \{ a,b,c,0,1\}$
2. $C \times B = \{ (x,y)|x \in C \wedge y \in B\} = \{ (0,x),\,(0,y),\,(1,x),\,(1,y)\}$
3. $B - A = \{ x|x \in B \wedge x \notin A\} = \{ x,y\} = B$
4. $A \cap C = \{ x|x \in A \wedge x \in C\} = \emptyset$ then $\left( {A \cap C} \right) \cup B = \emptyset \cup B = B = \{ x,y\}$