Math 112 5. Unions & Intersections

≤ Union: combine all the elelments of both sets

≥ Intersection: choose only those elements that are in both sets.

Let A = {1, 2, 3, 4 }

Let B = {2, 4, 6,8}

Let U = Universe = {1,2,3,4,5,6,7,8,9,10}

A' = the complement of A = {5,6,7,8,9,10}

Write the indicated set.

1. A ≤ B

2. A ≥ B

3. (B ≤ A) ≥ A

4. (A ≤ A') ≥ B

5. A' ≥ B'

6. B' ≤ A'

7.B’ ≤ A

8. A ≥ (B’≤ A’)

Express the answer both graphically and in interval notation.

1. x > 3 ≤ x > 5

2. x > 3 ≥ x > 5

3. x ≤ -6 ≥ x ≥ 2

4. x ≥ -3 ≤ x ≤ -8

5. 2 ≤ x < 4 ≥ x ≥ 4

6. 2 ≤ x ≤ 4 ≥ x ≥ 4

7. 1 < x < 3 ≤ 2 ≤ x < 7

8. -4 < x ≤ 5 ≥ 0 ≤ x < 8

Write as a single interval if possible

1. [3 , 5) ≥ ( 1 , 7]

2. ( -4 , 2] ≤ ( 1 , 3]

3. (-∞, 4] ≥ (0, 8]

4. ( -∞, -3] ≤ (-10, ∞ )

5. (∞ , 6] ≥ [3, ∞)