Introduction to logic sentences
In mathematical logic, a sentence is a predicate logic and a well formed formula with no free variables. A sentence is viewed by some as expressing a proposition. It makes an the assertion, potentially concerning any structure of L. This assertion has a fixed truth value with respect to the structure. In contrast, the truth value of a formula (with free variables) may be indeterminate with respect to any structure. As the free variables of an formula can range over several values (which could be members of a universe, relations or functions), its truth value may vary. And now let us see about the logic sentences.(Sources – Wikipedia).
Basic Concept of Logic sentences:
Logic is a set of sentences in a proper language. The logic sentences forms a theory are called its theorems. Logic involved in statements or propositions
Five Terms Propositional in logic sentences
Not
Or
And
If… then
If and only if
Some Operations in Logic sentences:
Negation (˜p): The proposition is true means then they can change into negative and vice versa.
Disjunction (pvq): The two of the propositions are negative then the result is false or else true.
Conjunction (p^q): The two of the propositions are right means then the result is true or else false.
Conditional (p→q): The Truth of the proposition ‘p’ is enough to truth of proposition ‘q’.
Bi-conditional (p↔q): ‘p’ is enough condition for ‘q’. ‘q’ is required for ‘p’. if not ‘q’ not ‘p’. Not ‘p’ unless ‘q’. Not ‘p’ without ‘q’.
Example problems:
Example 1:
A, B, can represent the Logical sentences. They represent some definite propositions.
For example:
A = "My shirt is white"
B = "The sun is Hot"
Now we get the final result are:
(A -> B)
But, if I were to dye my shirt for white on a Hot day, then the
Sentence (A -> B) would become negative.
Now the a logical sentence, such as:
(A -> B)
as discuss in above is true under some situation, and false under
other situation.
By distinguish, the logical argument:
A |- B
is *always* invalid.
Example 2:
What is the conjunction equation for the following statements?
P: Peter reading story book.
Q: Jenny reading newspaper.
Solution:
Given statement is as follows,
P: Peter reading story book.
Q: Jenny reading newspaper.
Conjunction is a ‘and’ declaration. The symbol of ‘and’ condition is ^.
We can write the above statement in the following format.
" Peter reading story book adn Jenny reading newspaper".
So logical equation = P ^ Q.
Example 3
Write the logical form for the following statement.
"Jenifer likes apples or oranges".
Solution:
Let P:Jenifer likes apples
Q:Jenifer likes oranges.
The 'or' condition represents the disjunction.
So logical form=PvQ.
Example 4
What is the conditional form for the following statements?
"If we go to the college early, then we can enter the class room without punishment".
Solution:
Given statement is as follows,
P: If we go to the college early
Q: then we enter the class room without punishment.
Conditional is an ‘if-then’ declaration. The symbol of ‘if-then’ condition is ‘→’.
So logical equation = P → Q.
Example 5
What is the logic form for the following statements?
"Alex drives a bike or car".
Solution:
Let P: Alex drives a bike.
Q: Alex drives a car.
The given declaration is ‘or’. The notation of ‘or’ is v.
Therefore the logical form=PvQ.
Practice problems:
Question 1:
What is the conjunction form of the following statements?
“ Peter has bicycle and bike”.
Question 2:
Write the logic form for the following statement?
“Jessie likes to play tennis or badminton”.
Question 3:
What is the logic form for the following statement?
"If u go to school then u will learn the english".
Answers:
1. Conjunction= P^Q
2. Disjunction =PvQ
3. Form =P→Q
These logic design questions are used to learn about the concepts.
In mathematical logic, a sentence is a predicate logic and a well formed formula with no free variables. A sentence is viewed by some as expressing a proposition. It makes an the assertion, potentially concerning any structure of L. This assertion has a fixed truth value with respect to the structure. In contrast, the truth value of a formula (with free variables) may be indeterminate with respect to any structure. As the free variables of an formula can range over several values (which could be members of a universe, relations or functions), its truth value may vary. And now let us see about the logic sentences.(Sources – Wikipedia).
Basic Concept of Logic sentences:
Logic is a set of sentences in a proper language. The logic sentences forms a theory are called its theorems. Logic involved in statements or propositions
Five Terms Propositional in logic sentences
Not
Or
And
If… then
If and only if
Some Operations in Logic sentences:
Negation (˜p): The proposition is true means then they can change into negative and vice versa.
Disjunction (pvq): The two of the propositions are negative then the result is false or else true.
Conjunction (p^q): The two of the propositions are right means then the result is true or else false.
Conditional (p→q): The Truth of the proposition ‘p’ is enough to truth of proposition ‘q’.
Bi-conditional (p↔q): ‘p’ is enough condition for ‘q’. ‘q’ is required for ‘p’. if not ‘q’ not ‘p’. Not ‘p’ unless ‘q’. Not ‘p’ without ‘q’.
Example problems:
Example 1:
A, B, can represent the Logical sentences. They represent some definite propositions.
For example:
A = "My shirt is white"
B = "The sun is Hot"
Now we get the final result are:
(A -> B)
But, if I were to dye my shirt for white on a Hot day, then the
Sentence (A -> B) would become negative.
Now the a logical sentence, such as:
(A -> B)
as discuss in above is true under some situation, and false under
other situation.
By distinguish, the logical argument:
A |- B
is *always* invalid.
Example 2:
What is the conjunction equation for the following statements?
P: Peter reading story book.
Q: Jenny reading newspaper.
Solution:
Given statement is as follows,
P: Peter reading story book.
Q: Jenny reading newspaper.
Conjunction is a ‘and’ declaration. The symbol of ‘and’ condition is ^.
We can write the above statement in the following format.
" Peter reading story book adn Jenny reading newspaper".
So logical equation = P ^ Q.
Example 3
Write the logical form for the following statement.
"Jenifer likes apples or oranges".
Solution:
Let P:Jenifer likes apples
Q:Jenifer likes oranges.
The 'or' condition represents the disjunction.
So logical form=PvQ.
Example 4
What is the conditional form for the following statements?
"If we go to the college early, then we can enter the class room without punishment".
Solution:
Given statement is as follows,
P: If we go to the college early
Q: then we enter the class room without punishment.
Conditional is an ‘if-then’ declaration. The symbol of ‘if-then’ condition is ‘→’.
So logical equation = P → Q.
Example 5
What is the logic form for the following statements?
"Alex drives a bike or car".
Solution:
Let P: Alex drives a bike.
Q: Alex drives a car.
The given declaration is ‘or’. The notation of ‘or’ is v.
Therefore the logical form=PvQ.
Practice problems:
Question 1:
What is the conjunction form of the following statements?
“ Peter has bicycle and bike”.
Question 2:
Write the logic form for the following statement?
“Jessie likes to play tennis or badminton”.
Question 3:
What is the logic form for the following statement?
"If u go to school then u will learn the english".
Answers:
1. Conjunction= P^Q
2. Disjunction =PvQ
3. Form =P→Q
These logic design questions are used to learn about the concepts.
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