Introduction to solving logic and set theory:
The word logic indicates analysis. Analysis may be approved result or mathematical proof. Basic logical connectives are AND, OR and NOT. The collections of elements are called as set. Basic operations of sets are union, intersection and complement. Let us see solving logic and set theory in this article.
Logic and set theory:
Logic:
The term logic denotes analysis. Analysis may be approved result or mathematical proof.
Logical statement:
Logical statement is a sentence which is any one true or false but not both.
Basic logical connectives:
* AND or conjunction
* OR / disjunction
* NOT or negation
AND or conjunction:
Another name of logical connective AND is conjunction.
We apply symbol to represent the logical connective AND.
Truth table for AND or conjunction:
A B A [^^] B
T T T
T F F
F T F
F F F
OR:
Another name of logical connective OR is disjunction.
We apply symbol to represent the logical connective OR.
Truth table for OR / disjunction:
A B A [vv] B
T T T
T F T
F T T
F F F
NOT:
Another name of logical connective NOT is negation.
We apply '~' symbol to represent the logical connective NOT.
Truth table for NOT or negation:
A ~A
T F
F T
Set theory:
Collection of objects is called as set theory.
Basic operations of set theory:
* Union
* Intersection
* Complement
Union:
The set of all the elements are presents in the union.
Intersection:
The common elements are presents in the intersection.
Complement:
Set of all the elements of U which are absent in given set is called as complement of given set.
Problems for logic and set theory:
Problem 1:
Do (A [^^] B) [vv] A
Solution:
Given
(A [^^] B) [vv] A
A B A [^^] B (A [^^] B) [vv] A
T T T T
T F F T
F T F F
F F F F
Problem 2:
Set A= {1, 2, 3, 4, 5, 6, 7} set B = {2, 4, 6, 8, 10} and set C = {3, 4, 6, 7, 8, 9, 10}
Find (A [uu] B), (A [nn] C), (B [uu] C)
Solution:
Given
A= {1, 2, 3, 4, 5, 6, 7}
B = {2, 4, 6, 8, 10}
C = {3, 4, 6, 7, 8, 9, 10}
A [uu] B= {1, 2, 3, 4, 5, 6, 7, 8, 10}
A [nn] C= {3, 4, 6, 7}
B [uu] C= {2, 3, 4, 6, 7, 8, 9, 10}
Works Cited
Introduction to study online logical equivalence:
Various websites are presented in online to study about the logical equivalence.
(Sketch 24) Show logical notation that expresses following statement: If one dice shows an even number of spots and the second dice show an odd number of spots, then the total for the pair is less than or equal to 9.
Mill, J. S. (2000). System of Logic Ratiocinative and Inductive. London: Longmans, Green, and Co.
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