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1.5 Intersection, Union, & Compound Inequalities. The intersection of two sets A and B is the set of all members that are common to A and B. A conjunction A ∩ B Read as: “ A and B ”. Examples. 1) {1,2,3,4} ∩ {2,3,7,8}
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The intersection of two sets A and B is the set of all members that are common to A and B. A conjunction A ∩ B Read as: “A and B”
Examples 1) {1,2,3,4} ∩ {2,3,7,8} = {2,3} 2) {x / x > -2} ∩ {x / x < 1} = {x / -2 < x < 1} 3) (-∞,-2] ∩ (4, ∞) = { }
When two sets have no elements in common, they are said to be disjoint. The solution is an empty set, { } or
The union of two sets A and B is the collection of all elements belonging to A and/or B. A disjunction A U B Read as “A or B”
Examples 1) {1,2,3,4} U {-1,0,1,2} = {-1,0,1,2,3,4} 2) {x / x ≤ -2} U {x / x > 4} = {x / x ≤ -2 or x > 4} 3) (-∞,2] U (-4, ∞) = (-∞,∞)
1 ≤ x and x < 3 Graph: Solution [1,3)
Solving compound inequalities 2) -1 ≤ 2x + 5 < 13 -5 - 5 -5 -6 ≤ 2x < 8 2 2 2 -3 ≤ x < 4 Graph Solution [-3,4)
3) 2x – 5 ≥ -3 and 5x + 2 ≥ 17 +5 +5 -2 -2 2x ≥ 2 5x ≥ 15 2 2 5 5 x ≥ 1 x ≥ 3 Graph Solution: [3, ∞)
4) x – 4 < -3 or x – 3 ≥ 3 + 4 +4 + 3 +3 x < 1 or x ≥ 6 Graph: Solution: (-∞, 1) U [6, ∞)
3x – 11 < 4 or 4x + 9 ≥ 1 + 11 +11 - 9 -9 3x < 15 4x ≥ -8 x < 5 x ≥ -2 Graph Solution: (-∞,∞)
- 3x - 7 < -1 or x + 4 < -1 + 7 +7 - 4 - 4 -3x < 6 x < - 5 -3 -3 x > -2 Graph Solution: (-∞,-5) U (-2, ∞)
