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Table of Contents Compound Inequalities When the word and is used we call it a conjunction. A compound inequality is formed when two inequalities are joined using either the word and or the word or. When the word or is used, it is called a disjunction.
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Table of Contents Compound Inequalities ConjunctionDisjunction AndOr
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Table of Contents Two more definitions are needed before we proceed. The intersection of two sets is the set of elements that are common to both sets. The symbol ∩ is used to represent intersection. The union of two sets is the set of elements that are in one or the other of the sets. The symbol U is used to represent union.
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Table of Contents Consider how two streets come together to demonstrate these concepts. The intersection of the two streets is the portion of pavement that is common to both. Harmony Street Shields Street
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Table of Contents The union of the two streets is the portion of pavement that is on one street or the other. Harmony Street Shields Street
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Table of Contents The union of the two streets is the portion of pavement that is on one street or the other. Harmony Street Shields Street Note that this includes the intersection which is on both streets.
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Table of Contents When working with a conjunction, think intersection. ConjunctionDisjunction AndOr Intersection
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Table of Contents When working with a disjunction, think union. ConjunctionDisjunction AndOr IntersectionUnion
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Table of Contents Example 1 Solve: This is a conjunction (and), so we want the intersection. Solve each of the inequalities.
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Table of Contents We want to find the values of x that are common to both inequalities. A graph will assist in accomplishing this.
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Graph the points on the line that are common to both graphs. The solution is The interval notation answer is
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Table of Contents Example 2 Solve: This is a disjunction (or), so we want the union. Solve each of the inequalities.
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Table of Contents We want to find the values of x that satisfy one inequality or the other. A graph will assist in accomplishing this.
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Table of Contents
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Graph the points on the line that are on one graph or the other. The solution is The interval notation answer is
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