Logic Slides

Question 1

Formal Logic

Answer 1

• Formal System of rules for how we should prove or disprove things
• Can be used to represent the statments that we use in English to communicate facts or information

Question 2

Statements

Answer 2

A sentence that is true or false NOT both

Question 3

Truth Value

Answer 3

True = T(1)
False n= F(0)

Question 4

Compound Statements

Answer 4

Statement made of more than one simple statement
- Usually use some kind of logical connectives

Question 5

Components of Compound Statements

Answer 5

• Statement Variables : A, B, C
• Logical Connectives: ∨, ∧, →, ↔, ¬

Question 6

Conjuction

Answer 6

∧ (AND)
A ∧ B : “A and B”

Question 7

Disjuction

Answer 7

OR
A ∨ B: “A or B”

Question 8

Negation

Answer 8

¬ NOT
¬ A : “Not A”

Question 9

Implication

Answer 9

→ IF
A → B : “If A then B” or “A implies B”
A : Hypothesis
B : Conclusion

Question 10

Equivalence

Answer 10

↔ If and only if
A ↔ B : “A if and only if B”

Question 11

Well formed formulas (WFF)

Answer 11

Combined variables, connectives, and parentheses make an expression that is meaningful.

Question 12

Order of Precedence

Answer 12

1. Connectives parentheses, innermost parenthese first
2. Negation
3. Conjuction, disjunction
4. Implication
5. Equivalence

Question 13

Number of Rows in a Truth Table

Answer 13

2^n

Question 14

Tautology

Answer 14

A wff that is intrinsically true, no matter what statements comprise the wff

Question 15

Contradictions

Answer 15

A wff that is intrisically false, no matter what the truth statements that compromise the wff

Question 16

Propostions

Answer 16

Also known as statements.

Question 17

Logical Equivalences

Answer 17

Two statements forms are logically equivalent if and only if they have identical truth values for each possible substitution of statements for their statement variables.
Denotes 𝑃 ≡ 𝑄
- Used to simplify statements