Propositional Logic 1

Question 1

Logic is the science of…

Answer 1

reasoning.

Question 2

_ reasoning and _ are based on the _ of logic.

Answer 2

Mathematical, arguments, rules

Question 3

Reasoning is how we process…

Answer 3

our thinking in a logical way.

Question 4

Logic contains…

Answer 4

propositions.

Question 5

Propositions should be _ sentences, either _ or _.

Answer 5

declarative, true, false

Question 6

Propositions cannot be _ or _ at the same time.

Answer 6

true, false

Question 7

Propositions cannot be _ or _ at the same time.

Answer 7

true, false

Question 8

Propositions cannot be 50%…

Answer 8

true or false.

Question 9

Propositions cannot be a phrase or _.

Answer 9

onomatopoeia

Question 10

Propositions should have a _ in equations.

Answer 10

quantifier

Question 11

What is the foundation of logic?

Answer 11

Propositions.

Question 12

These are letters that can represent propositions.

Answer 12

Propositional variables.

Question 13

Compound propositions are combinations of…

Answer 13

1 or more propositions with logical connectives or operators.

Question 14

These are also used in logic and computer languages.

Answer 14

Operators.

Question 15

What is the symbol for negation?

Answer 15

”~” or “¬”.

Question 16

A truth table is a tabular representation of all _ _ for _ and outputs.

Answer 16

value combinations, inputs

Question 17

A truth table provides _ _ for results of applying an _ on each possible _ of _ _ for the operands.

Answer 17

truth values, operand, set, truth values

Question 18

What are the symbols for conjunction?

Answer 18

“&”, “^”, or “*”.

Question 19

A conjunction forms compound propositions with _ to join them.

Answer 19

“and”

Question 20

_ can also be used in place of “and”.

Answer 20

“But”

Question 21

A disjunction forms compound propositions with _ to join them.

Answer 21

“or”

Question 22

What is the symbol for disjunction?

Answer 22

“v”.

Question 23

“v” is called _.

Answer 23

“vel”

Question 24

How does the precedence of operators go?

Answer 24

1. ()
2. ~
4. v
5. ⊕
6. →
7. ↔

Goes from left to right if the same operators are present.

Question 25

An exclusive disjunction is also known as an exclusive _.

Answer 25

OR

Question 26

What are the other ways to write ⊕?

Answer 26

1. XOR 2. EOR 3. EXOR 4. Direct sum

Question 27

An exclusive disjunction can usually be _.

Answer 27

or | But not both.

Question 28

What is the rule in exclusive disjunction?

Answer 28

Compound propositions are true if one is true. Otherwise, false.

Question 29

"If p then q" is a _ statement.

Answer 29

conditional

Question 30

In a conditional statement, the p can be denoted as...

Answer 30

premise, hypothesis, and antecedent.

Question 31

In a conditional statement, the q can be denoted as...

Answer 31

conclusion, and consequent.

Question 32

What is the rule in conditional statements?

Answer 32

All compond propositions are true except when true implies false.

Question 33

In constructing a truth table, the amount of rows increase _ as more propositions are added.

Answer 33

exponentially ## Footnote n proposition = 2^n rows.

Question 34

How is p↔q read?

Answer 34

"p if and only if p".

Question 35

Biconditional statements are called...

Answer 35

bi-implication, or biconditional of p and q.

Question 36

Biconditionality is also known as...

Answer 36

logical equality.

Question 37

What is the rule in biconditionality?

Answer 37

Compound propositions are true if both are the same. Otherwise, false.

Question 38

Tautology is an always...

Answer 38

true logical expression.

Question 39

Contradictions are also known as...

Answer 39

fallacies, or unsatisfiable.

Question 40

Contradictions are always...

Answer 40

false.

Question 41

What is a contingency?

Answer 41

It is neither a tautology nor a contradiction.