discrete_mathematics_with_applications/chapter_1/test_yourself.md

Test Yourself

Page 28

1. A universal statement asserts that a certain property is _______ for _______.

2. A conditional statement asserts that if one thing _______ then some other thing _______.

3. Given a property that may or may not be true, an existential statement asserts that _______ for which the property is true.

Solutions:

1. true, for all elements of a set.

2. is true, also has to be true.

3. there is at least one thing

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Test Yourself

Page 37

1. When the elements of a set are given using the set-roster notation, the order in which they are listed _______.

Solution

does not matter.

2. The symbol \mathbb{R} denotes _______.

Solution

The set of all real numbers.

3. The symbol \mathbb{Z} denotes _______.

Solution

The set of all integers.

4. The symbol \mathbb{Q} denotes _______.

Solution

The set of all rational numbers.

5. The notation \{x | P(x)\} is read _______.

Solution

The set of all x such that P(x) is true.

6. For a set A to be a subset of a set B means that _______.

Solution

Every element in A is an element in B.

7. Given sets A and B, the Cartesian product A \times B is _______.

Solution

The set of all ordered pairs (a, b) where a \in A and b \in B.

8. Given sets A, B, and C, the Cartesian product A \times B \times C is _______.

The set of all ordered triples, (a, b, c) where a \in A and b \in B and c \in C.

Solution

9. A string of length n over a set S is an ordered $n$-tuple of elements S, written without _______ or _______.

Solution

parentheses; commas