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5th Edition

EPP + 1 other

Publisher: Cengage Learning,

ISBN: 9781337694193

Chapter 6.2, Problem 6ES

Textbook Problem

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Let
*A, B, *and *C, *
*. *

Proof: Suppose *A*, *B *and *C *are any sets.

(1) Proof that

Let
*[We must show that *
__(a) __*].*

By definition of
__(b) __and

Thus
__(c) __.

*Case 1 *(

*Case 2 *(

By cases 1 and 2,
__(d) __.*[So *
*by definition of subset.](2) Proof that *

Let

By definition of
__(a) __

*Case 1 *

Since

*Case 2 *
__(b) __

Since

In both cases
__(c) __.

*[So *
*by definition of (d) .]* (3)

To determine

**(a)**

**To fill:**

The given blanks in the proof that

**Given:**

Let

- Now we must show that ________(a)________

By definition of

Thus

**Case 1**

**Case 2**

By cases 1 and 2, __,______(d)________.__

**Concept used:**

- If an element

If an element

And

**Proof:**

- Let

Now we must show that

By definition of

To determine

**(b)**

**To fill:**

The given blanks in the proof that

To determine

**(c)**

**To fill:**

The given blanks in the proof that

Discrete Mathematics With Applications

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