discrete_mathematics_with_applications/chapter_2/test_yourself.md

Test Yourself

Page 73

1. An and statement is true when, and only when, both components are _______.

Solution

True.

2. An or statement is false when, and only when, both components are _______.

Solution

False.

3. Two statement forms are logically equivalent when, and only when, they always have _______.

Solution

The same truth values.

4. De Morgan's laws says (1) that the negation of an and statement is logically equivalent to the _______ statement in which each component is _______, and (2) that the negation of an or statement is logically equivalent to the _______ statement in which each component is _______.

Solution

or; negated; and; negated.

5. A tautology is a statement that is always _______.

Solution

true

6. A contradiction is a statement that is always _______.

Solution

false