Question

Let A = {x ∈ R : x 2 = 2} and B = {x ∈ R : x ≥ 0}.

1. Find A ∩ B.

2. Find A ∪ B.

3. Find A − B.

4. For U = R, find Ac and Bc .

5. Find N − B.

Answer 1

1.

$$A\cap B=\{\sqrt{2}\}$$

2.

$$A\cup B=\{x ∈ R : x ≥ 0\ or\ x=-\sqrt{2}\}$$

3.

$$A- B=\{-\sqrt{2}\}$$

4.

$$A^C=\{x ∈ R : x^ 2 \not= 2\}$$

$$B^C=\{x ∈ R : x<0\}$$

5.

The set of natural numbers

$$\N = \{0, 1, 2, 3, . . .\}$$

$$\N-B=\empty$$