Intro to Discrete Math

Question 1

Give examples of discrete objects

Answer 1

Integers (whole numbers), rational numbers (quotient of two integers), automobiles, houses, people

Question 2

This category of mathematics is based upon a continuous number line. It is characterized by the fact that between any two numbers, there are almost always an infinite set of numbers.

Answer 2

Continuous Mathematics

Question 3

This category of mathematics involves distinct values.

Answer 3

Discrete Mathematics

Question 4

Give five connectives used in a propositional logic

Answer 4

Or (v)
And (^)
Negation (¬)
Implication/if-then (→)
If and only if (↔)

Question 5

Condition: The proposition is true if at least any of the propositional variable A or B is true

Answer 5

OR (v)

Question 6

Condition: Both propositional variables A and B are true

Answer 6

And (^)

Question 7

Condition: Unless the propositional variables A and B are equal, the second variable is the truth value

Answer 7

Implication

Question 8

Condition: The proposition is only true of both propositional variables are the same

Answer 8

If and only if

Question 9

This is a formula which is always true for every value of its propositional variables

Answer 9

Tautology

Question 10

This is a formula which is always false for every value of its propositional variables

Answer 10

Contradiction

Question 11

This is a formula which has both some true and some false values for every value of its propositional variables

Answer 11

Contingency

Question 12

This is the negation of both the hypothesis and the conclusion

(p→q) = (¬p→¬q)

Answer 12

Inverse

Question 13

The is computed by interchanging the hypothesis and the conclusion

(p→q) = (q→p)

Answer 13

Converse

Question 14

This is computed by interchanging the hypothesis and the conclusion of the inverse statement

(p→q) = (¬q→¬p)

Answer 14

Contrapositive