An Approach to Algebra
Claudia Patricia Chapa Tamez
Example 1.3.3 Disjoint, equal and
equivalent sets
Determine if the given sets are disjoint, equal or equivalent.
1) A={xZ|3<x<11} and B={x|x is a day of the week}
2) A={1,2,3,4,5} and B={6,7,8,9,10}
3) A={0,1,2,3,4,5,6,7,8,9} and B={x|x is a digit}
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An Approach to Algebra
Claudia Patricia Chapa Tamez
Solution
Determine if the given sets are disjoint, equal or equivalent.
1) If A={xZ|3<x<11} and B={x|x is a day of the week}, then a recommendation is to
express sets in roster form A={4,5,6,7,8,9,10}, then find n(A) = 7 and B={Monday,
Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}, then find n(B)=7. Since
n(A)=7 and n(B)=7, then AB , which means that they are equivalent sets.
2) If A={1,2,3,4,5} and B={6,7,8,9,10},then A and B are disjoint sets, since they don’t
have elements in common.
3) If A={0,1,2,3,4,5,6,7,8,9} and B={x|x is a digit}, then they both have exactly the same
elements, so they are said to be equal sets, no matter that they’re expressed in different
forms, roster and set builder form.
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