1. What is symbolic logic? Discuss the characteristics of symbolic logic.
Answer: Symbolic logic is the branch of logic that is established through the extensive use of symbols for the purpose of expressing logic and determining its true value. The characteristics of symbolic logic are:
(1) The use of conceptual signs.
(2) Application of deductive methods.
(3) Use of variable or variable symbols.
2. Is there any relationship between symbolic logic and mathematics?
Answer: There is a relationship between symbolic logic and mathematics. The development of symbolic logic is inextricably linked to the development and progress of mathematics. Modern mathematicians and modern symbolic logicians have shown that modern mathematics and symbolic logic are essentially the same subject matter, size and method of study.
3. Explain the advantages or utilities of using symbols in symbolic logic.
Answer: The advantages or uses of using symbols in symbolic logic are:
(1) The use of symbols helps to classify the argument by expressing its size.
(2) The use of symbols expresses the universality of logical rules.
(3) The use of symbols helps to express complex statements or arguments clearly and simply on a small scale.
4. Define the following:
(a) Change
Answer: Symbols that can take on variable values within a certain range are called variables.
(b) Conceptual signs
Answer: Signs or symbols that directly represent ideas and indirectly represent sounds or words are called conceptual signs.
(c) Deductive method.
Answer: Deduction is the method of establishing a large number of sentences by applying a small number of rules from a small or limited number of sentences.
5. Give examples of the following:
(a) Change
Answer: 1,2,3
(b) Conceptual signs
Answer: +, ×, ,
6. Fill in the blanks:
(a) Symbolic logic is formal and deductive like mathematics .
(b) Conceptual signs directly indicate concepts .
(c) Symbolic logic is entirely formal in nature .
(d) Symbolic logic is an extension of traditional logic .
(e) An additive function pq is true when both the additives p and q are true .
(f) A support function p≡q is true when the truth-values of the two variables it contains are true .
(g) Each argumentative conjunction adds only simple sentences.
(h) All truth-values below the principal invariant symbol of a 'logical false' statement will be false .
7. Answer briefly:
(i) What is a deductive method?
Answer: Deductive method is the method of obtaining an indefinite number of statements from a given number of statements by applying certain rules.
(ii) What is meant by logical invariant symbols?
Answer: Symbols that express the size of compound statements and express the same meaning every time they are used according to the verbal form are called logical invariant symbols.
(iii) What is a true function? Name the basic truth-functions and provide a truth-list of each?
Answer: A truth function is a compound statement containing variables and the truth value of the essence is determined based on the truth value of the variable.
The names of the basic truth functions are:
(i) Negative function (P)
(ii) additive function (pq)
(iii) Optional negative function (pvq)
(iv) significance or implication function (p⊃q)
(v) synonymous function (p≡q)
(iv) Why are basic truth-functions called 'basic'?
Answer: Fundamentals are called fundamentals because other more compound truth-functional statements are formed on the basis of this basic truth-function.
8. Examine the following compound statements and choose the constants in them.
(a) If Rita comes, Rupa Rupa will go.
Answer: If, and.
(b) The weather is bright and clear.
Answer: And.
(c) He bought a pair of clothes but no shoes. (Consider 'but' as support for 'and').
Answer: But.
(d) If it does not rain, the grass will not get wet and the game will not have to be cancelled.
Answer: And.
(e) It is false that he is shy and boring.
Answer: False.
(f) If India lose the match, the team will be changed.
Answer: Then.
(g) The people of this country are also honest and hardworking.
Answer: And.
