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Chapter 6: Problem 38

Determine whether the pairs of sets are disjoint. a. \(\varnothing,\\{1,3,5\\}\) b. \(\\{0,1,3,4\\},\\{0,2,5,7\\}\)

Short Answer

Expert verified
The first pair of sets, \(\varnothing\) and \(\{1,3,5\}\), is disjoint as the empty set has no elements. The second pair of sets, \(\{0,1,3,4\}\) and \(\{0,2,5,7\}\), is not disjoint since they have the common element 0.

Step by step solution

01

Identify the Pairs of Sets

There are two pairs of sets given: a. \(\varnothing,\\{1,3,5\\}\) b. \(\\{0,1,3,4\\},\\{0,2,5,7\\}\)
02

Check for Common Elements in the First Pair of Sets

In the first pair of sets, one set is the empty set (\(\varnothing\)) which contains no elements, and the other set is \(\{1,3,5\}\). Since the empty set has no elements, it cannot have any common elements with any other set. Therefore, the first pair of sets is disjoint.
03

Check for Common Elements in the Second Pair of Sets

In the second pair of sets, we have: Set A = \(\{0,1,3,4\}\) and Set B = \(\{0,2,5,7\}\) To determine if these sets are disjoint, we need to check if they have any common elements. We can see that both Set A and Set B have the element 0. Since they have a common element, the second pair of sets is not disjoint. In conclusion, the first pair of sets is disjoint, while the second pair of sets is not disjoint.

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Most popular questions from this chapter

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