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Class 11 Logic And Philosophy Chapter 9 Symbolic Logic
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Symbolic Logic
Chapter – 9
LOGIC & PHILOSOPHY
VERY SHORT TYPES QUESTIONS AND ANSWERS
1. What is symbolic logic? Discuss the characteristics of symbolic logic?
Ans : Symbolic Logic is that branch of logic which uses symbols to bring out features of logical importance in arguments and so to classify them into types to which we can apply general rules and find out the validity of arguments.
The three main characteristics of symbolic logic are : (a) The use of ideograms, instead of phonograms.
(b)The use of deductive method i.e. from a small number of statements we can generate, by applying rules, indefinite number of other statements.
(c)The use of variables, which have definite range of significance.
2. Is there any relation between symbolic logic and mathematics?
Ans : Symbolic logic has a close relation with mathematics. That is why symbolic logic is also known as mathematical logic. Aristotle had introduced the notion of a variable for the first time. The of variables in elementary mathematics is too familiar. The use of variables is widely used by symbolic logicians. The three main characteristics of symbolic logic viz. (1) the use of ideograms (2) the use of deductive method (3) the use of variables, are also characteristics of mathematics. Thus the development of symbolic 4. logic has been bound up with the development of mathematics. (a Thus we see that all the pioneers of symbolic logicians were at bottom mathematicians.
3. Explain the advantages of the use of symbols in symbolic logic.
Ans : Symbolic logicians used symbols to avoid some difficulties of language. In our day-to-day life we express our thoughts in sentences. The use of symbols exhibits the logical form of the argument according to its form. By which validity can be determined in arguments. By applying general rules to the form of argument testing would be easy.
The use of symbols helps to express the generality of the logical rules. Logical rules are general in nature applicable to all the arguments of a particular form.
The use of symbols ensures the clarity, consciousness and economy of expression to complicated logical statements, which is unintelligible when expressed in ordinary language.
The use of symbols helps to express conveniently the concepts and techniques, which are peculiar to logic. Symbols like variables are also useful to represent logical operations.
The use of symbols helps to avoid the difficulties arising out of the use of ordinary language like ambiguity, obscurity, etc.
The use of symbols helps to protect the argument from the influence of the material truth or falsity of the constituent propositions. Symbolic logic puts emphasis on formal truth rather than material truth. By the use of symbols, the difficulties in the determination of the validity of the argument can be avoided and helps the mind to concentrate on the validity and invalidity of the argument.
4. Define the following :
(a) Variable.
Ans : A variable is a symbol which can stand for any one of a given range of values.
(b) Ideograms.
Ans : Ideograms are signs which stand directly for concepts.
(c) Deductive method.
Ans : The method of deducing an indefinite number of statements from a definite number of statements from a definite number by the application of the limited number of rules is called deductive method.
5. Give example of the following :
(a) Variable.
Ans : ‘X’ is a variable, which ranges over the real numbers.
(b) Ideograms.
Ans : The multiplication sign (x) or the question mark (?) are the ideograms.
6. Fill up the blanks :
(a) Symbolic logic is………….. and …………. like mathematics.
Ans : Formal, deductive.
(b) Ideograms directly stand for…………….
Ans : Concepts.
(d) Symbolic logic is completely……………. in nature.
Ans : Formal.
(d) Symbolic logic is the…………form of the traditional deductive logic.
Ans : developed.
(e) A conjunctive function p.q. is true when both the conjuncts p and q are…………..
Ans : true.
(f) A biconditional function p=q the truth values of its constituent propositions have the………….truth value.
Ans : Same.
(g) Every connective connects only…………. propositions.
Ans : two.
(h) All the truth-values under the main constant of a valid statement will be …………
Ans : true.
(i) All the truth-values under the main constant of an invalid statement will be……………….
Ans : false.
| Sl. No. | Contents |
| Unit – 1 | Logic |
| Unit – 2 | Proposition |
| Terms | |
| Proposition | |
| Transformation of Ordinary Sentences to Logical Proposition | |
| Distribution of a term is a logical Proposition | |
| Modern Classification of Proposition | |
| Unit – 3 | Inference, Categorical Syllogism |
| Inference | |
| Categorical Syllogism | |
| Unit – 4 | Symbolic Logic |
| Unit – 5 | Philosophy |
| Unit – 6 | Indian Philosophy |
| Unit – 7 | Theory of Knowledge |
| Rationalism & Empiricism | |
| Pramāna: Pratyaksa and Anumana | |
| Unit – 8 | Realism and Idealism |
| Realism | |
| Idealism |
7. Answer briefly :
(a) What is meant by deductive method?
Ans : The method of deducing an indefinite number of statements from a definite number of given statements by the application of the limited number of rules is called deductive method.
(b) What do you mean by logical constants?
Ans : Constants are symbols, which express the form of the compound expressions and maintain the same meaning throughout every occurence in the propositional formulae.
(c) What is truth-function? State the name of its basic forms by giving truth tables for each of them.
Ans : Truth-function is a compound expression which contains variables and whose truth-value is determined solely by the truth values of its component variables.
The basic truth functions and truth tables are as follows :
1. Negative function-~ p :
| p | ~p |
| T | F |
| F | T |
2. Conjunctive function-p.q :
| p | q | p.q |
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |
3.Disjunctive function-pvq :
| p | q | pvq |
| T | T | T |
| T | F | T |
| F | T | T |
| F | F | F |
4. Implicative function-p⊃q :
| p | q | p⊃q |
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |
5. Equivalent function-p≡q :
| p | q | p≡q |
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | T |
(d) Mention the truth tables of disjunctive function.
Ans : Truth Table of Disjunctive function :
| p | q | pvq |
| T | T | T |
| T | F | T |
| F | T | T |
| F | F | F |
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