Topic 7: Basic Form Logical Concepts

Question 1

Define Truth Value

Answer 1

Every declarative sentence has a truth value which means that the sentence is either true or false.

Question 2

Define Truth - Functional

Answer 2

The truth value of the sentence is determined by the truth value of its component sentences

Question 3

Truth function of a Negation

Answer 3

The negation of a sentence asserts the opposite of that sentence:

T | F
F | T

Question 4

Truth function of a Conjunction

Answer 4

Both conjunctions are true:

  P  |  Q  |  P and Q 
--------------------------
  T  |  T  |      T
  T  |  F  |      F  
  F  |  T  |      F
  F  |  F  |      F

Question 5

Truth function of a Disjunction

Answer 5

In an inclusive sense the disjunction asserts that at least one is true:

  P  |  Q  |  P or Q 
--------------------------
  T  |  T  |      T
  T  |  F  |      T
  F  |  T  |      T
  F  |  F  |      F

Question 6

Truth function of a Conditional Argument

Answer 6

Conditional implies that the antecedent is true then the conclusion is true:

  P  |  Q  |  If P, then Q 
-----------------------------
  T  |  T  |          T
  T  |  F  |          F  
  F  |  T  |          T
  F  |  F  |          T

  P  |  Q  |  P if and only if Q 
-------------------------------------
  T  |  T  |              T
  T  |  F  |              F  
  F  |  T  |              F
  F  |  F  |              T

Question 7

What are the three types of logical properties of a sentence?

Answer 7

i) Being Contingent
ii) Being Tautological
iii) Being Inconsistant

Question 8

What does it mean by “being contingent”?

Answer 8

A sentence that can be true or false.

For example:
P or Q

Question 9

What does it mean by “being tautological”?

Answer 9

“A sentence that is always true.

For example:
P or Not P
If P, Then P”

Question 10

What does it mean by “being inconsistent”?

Answer 10

“A sentence that is always false (similar to self-contradiction)

For example:
P and Not P
P if and only if Not P”

Question 11

What does Entailment mean?

Answer 11

A sentence is entailed when P follows logically to Q; which means that if P is true then Q must also be true

Question 12

How would you identify whether a statement is entailed by each other?

Answer 12

Within a truth table when one sentence is T the other must be T (T -> T or F ->F)

Question 13

In tautology what can be entailed?

Answer 13

Tautology can be entailed BY any sentence what so ever

Question 14

In an inconsistent sentence what can be entailed?

Answer 14

Inconsistent sentences can entail any sentence

Question 15

How would you find a sentence through natural deduction?

Answer 15

Put to standard form then write the conditions for each conclusion made