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, ∞)