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# Show that if A is an infinite set, then whenever B is a ISBN: 9780073383095 37

## Solution for problem 45E Chapter 2.2

Discrete Mathematics and Its Applications | 7th Edition

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Problem 45E

Show that if A is an infinite set, then whenever B is a set. A ? B is also an infinite set.

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Step 1 of 3

Solution:Step1To findWe have to show that if A is an infinite set, then whenever B is a set. A B is also an infinite set.Step2The union of sets A and B can be written asWe have to take all possible cases of set B.Case1:-Suppose A be an infinite set and B= then =AHence, A is an infinite set.Case2:-Assume B=A then is an infinite set.Case3:-Assume B is a finite set thenIs also an infinite set because A is infinite.So, will always infinite.Case4:-Assume if B is an infinite set thenIs also an infinite set as A and B are infinite sets.So, will be also infinite.Hence, from above all the cases it is clear that is an infinite set.

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Step 3 of 3

##### ISBN: 9780073383095

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Show that if A is an infinite set, then whenever B is a