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Class 11 Maths Chapter 14. Mathematical Reasoning
Logic
Logic is the subject that deals with the method of reasoning. It provides us rules for
determining the validity of a given argument in proving theorem.
Statement (Proposition)
A statement is an assertive sentence which is either true or false but not both a true statement is
called valid statement. Otherwise it is called invalid statement. Statements are denoted by the
small letters
i.e., p, q, r … etc.
Open and Compound Statement
A sentence which contains one or more variable such that when certain values are given to the
variable it becomes a statement, is called an open statement.
If two or more simple statements are combined by the use of words such as ‘and’, ‘or’, ‘not’,
‘if’, ‘then’, ‘if and only if ‘, then the resulting statement is called a compound statement.
Truth Value and Truth Table
A statement can be either ‘true’ or ‘false’ which are called truth values of a .statement and it is
represented by the symbols T and F, respectively.
A. truth table is a summary of truth values of the resulting statements for all possible
assignment of values to the variables appearing in a compound statement.
Number of rows depends on their number of statements.
Truth Table for Two Statements (p, q)
Number of rows = 22 = 4
pq
TT
TF
FT
FF
Elementary Operation of Logic
Class 11 Maths Chapter 14. Mathematical Reasoning
Logic
Logic is the subject that deals with the method of reasoning. It provides us rules for
determining the validity of a given argument in proving theorem.
Statement (Proposition)
A statement is an assertive sentence which is either true or false but not both a true statement is
called valid statement. Otherwise it is called invalid statement. Statements are denoted by the
small letters
i.e., p, q, r … etc.
Open and Compound Statement
A sentence which contains one or more variable such that when certain values are given to the
variable it becomes a statement, is called an open statement.
If two or more simple statements are combined by the use of words such as ‘and’, ‘or’, ‘not’,
‘if’, ‘then’, ‘if and only if ‘, then the resulting statement is called a compound statement.
Truth Value and Truth Table
A statement can be either ‘true’ or ‘false’ which are called truth values of a .statement and it is
represented by the symbols T and F, respectively.
A. truth table is a summary of truth values of the resulting statements for all possible
assignment of values to the variables appearing in a compound statement.
Number of rows depends on their number of statements.
Truth Table for Two Statements (p, q)
Number of rows = 22 = 4
pq
TT
TF
FT
FF
Elementary Operation of Logic
