Chapter 1.4, Problem 3TFE

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8th Edition

Gilbert + 2 others

ISBN: 9781285463230

Textbook Problem

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Label each of the following statements as either true or false.

Let

To determine

Whether the statement, “Let

Explanation

**Formula used:**

Suppose that

**Explanation:**

Let

By using the definition of power set,

(i) When both sets have the same elements,

In a similar way, when both sets have the same element, their intersection is the set itself.

(iii) When one of the sets is empty.

Similarly, intersection of one empty and other non-empty set is the same â€“ always an empty set.

(iii) When both sets are disjoint.

In a similar way, intersection of two disjoint sets is the empty set.

(iv) If one set is a proper subset of other.

That is, if one set is a proper subset of other, then their intersection is the same as the proper subset.

(v) Two different sets with non-empty intersection.

Thus, when two sets are different with non-empty intersection, then their intersection is all common elements of both the sets

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