Lesson 1: Foundation: Logic And Proofs

Question 1

is the study of mathematical structures that are countable or otherwise distinct or separable

Answer 1

Discrete Mathematics

Question 2

encompasses a wide array of topics that can be used to answer many tangible question

Answer 2

Discrete Mathematics

Question 3

Enumeration: DISCRETE MATHEMATICS CAN BA USED FOR?

Answer 3

1. Logic
2. Number Theory
3. Counting
4. Probability
5. Recurrences
6. Graph Theory

Question 4

traditionally defined as the study of laws of thought and correct reasoning

Answer 4

Logic

Question 5

usually understood in terms of inferences or arguments

Answer 5

Logic

Question 6

basis of all mathematical reasoning and all automated reasoning

Answer 6

Logic

Question 7

is a declarative sentence, that is declares a fact, either true or false but not both

Answer 7

Proposition

Question 8

studies the ways statements can interact with each other

Answer 8

Propositional Logic/ Propositional Calculus

Question 9

represented by small alphabets such as p, q, r, s

Answer 9

Propositional Variable

Question 10

formed from existing proposition using logical operators

Answer 10

Compound Proposition

Question 11

logical operators that are used to form a new proposition from two or more existing proposition

Answer 11

Connectives

Question 12

Enumerate: LIST OF LOGICAL CONNECTIVES

Answer 12

1. Negation
2. Conjunction
3. Disjunction
4. Conditional
5. Bi-Conditional

Question 13

it display the table of Compound Proposition

Answer 13

Truth Table

Question 14

The negation of the proposition can also be considered the result of the operation of the _________ on a proposition

Answer 14

Negation Operator

Question 15

is indicated by the symbol ^

Answer 15

Conjunction

Question 16

is indicated by the symbol v

Answer 16

Disjunction

Question 17

a Disjunction is false when both are true and both are false

Answer 17

Exclusive or

Question 18

a Disjunction is true when at least one of the two proposition is true

Answer 18

Inclusive or

Question 19

is indicated by the symbol ->

Answer 19

Conditional Statement

Question 20

If there is a proposition that has a form of if p then q, then that type of proposition will be called _________ or _________

Answer 20

Implication; Conditional Proposition

Question 21

In proposition if p then q, the p will be called ________ and q is _________

Answer 21

Hypothesis; Conclusion

Question 22

Conditional Statement is also called _________

Answer 22

Implication

Question 23

is indicated by the symbol <–>

Answer 23

Bi-conditional/ Double Implication

Question 24

helps to decide which operator will get evaluated first in a complicated looking compound proposition

Answer 24

Precedence of Operators

Question 25

Enumerate: PRECEDENCE OF OPERATORS(IN ORDER)

Answer 25

1. Negation
2. Conjunction
3. Disjunction
4. Implication
5. Bi-conditional

Question 26

truthtable probability formula with 2 possibilities (true/false)

Answer 26

2^n