Symbolic Logic Set Theory Table is a formal document that provides a comprehensive overview of set theory in symbolic logic. It presents key concepts, definitions, and symbols used in set theory, along with logical operations and relations. This table serves as a valuable reference for those studying or working with symbolic logic and set theory.
Symbolic Logic Set Theory Table
Symbolic logic set theory table in which we use mathematical symbol in short. we use different symbol in mathematical term is shown in the table.
Explanation of the use of the symbol.
Negation: ∼p
| p | ∼p |
| T | F |
| F | T |
If p is any proposition its negation is denoted by ∼p , read as , not p , . and if p is false , ∼p is true. The adjoining table, called truth table, gives the possible truth values of p and ∼p.
2; Conjunction of two statements p and q is denoted symbolically as p ∧ q ( p and q).A conjunction is considered to be true only if both its components are true. So the truth table of p ∧ q is in table
| p | q | p ∧ q |
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |
Example:1
i) Lahore is the capital of Punjab And Quetta is the capital of Baloachistan.
ii) 4 < 5 ∧ 8 < 10
iii) 4 < 5 ∧ 8 > 10
iv) 2 + 2 = 3 ∧ 6 + 6 = 10
Clearly conjunction i) and ii) are true, Where as iii and iv are false.
3 )Disjunction:
Disjunction of p and q is p or q. it is symbolically written as
The disjunction p ∨ q is considered to be true when at least one of the component p and q is true. it is false when both of them are false.
| p | q | p ∨ q |
| T | T | T |
| T | F | T |
| F | T | T |
| F | F | F |
Example : 2
i) 10 is the positive integer or 0 is rational number.
Find truth value of this dis junction.
Solution:
since the first component is true, the disjunction is true.
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