Correct symbolization of the following proposition is — “All successful politicians and orators are hard-working”.
(X) [Sx . (Px ∨ Ox) ⊃ Hx]
The proposition “All successful politicians and orators are hard-working” is a universal affirmative. It says of every individual x: if x is successful and is either a politician or an orator, then x is hard-working.
The word “and” here does not describe one individual who is both politician and orator; it means the claim holds for successful politicians and also for successful orators. Following Copi, such a subject is symbolised with a disjunction: (Px ∨ Ox).
Because it is a universal (A-type) proposition, the main connective inside the quantifier must be the horseshoe ⊃, giving (X) [Sx . (Px ∨ Ox) ⊃ Hx].
The other forms fail: (X) [Sx . Px . Ox] ⊃ Hx wrongly requires one person to be both politician and orator and leaves Hx outside the scope of the quantifier; (X) (Sx) . [(X) (Px . Ox) ⊃ Hx] wrongly asserts that everything is successful; (X) [Sx . (Px ∨ Ox) . Hx] uses conjunction, asserting that everything is a successful, hard-working politician or orator.
Hence, the answer is (X) [Sx . (Px ∨ Ox) ⊃ Hx].
Similar Questions
Match List I and List II and select the correct answer from the codes given below :
List I List II (a) ~ (p ∨ ~ p) (1) Identity (b) ~ (p • ~ p) (2) Contingency (c) ~ (p ⊃ q) (3) Tautology (d) p ⊃ p (4) Contradiction Codes :
(a) (b) (c) (d)
Which of the following is not the characteristics of an effective decision procedure ?
Correct formulation of the Rule U.I. (Universal Instantiation) is ........... .
Law of contradiction states that :
Characteristics of an Axiomatic systems are ................. .
(1) Consistency
(2) Completeness
(3) Independence
(4) Contingent
“Sudhir had not locked the gates yesterday. Either the watchman or Sudhir locks the gates. Therefore, the watchman must have locked the gates yesterday”. This argument is ..................... .
If the statement ‘p’ is true and the statement ‘q’ is false, the truth value of the statements ‘p ≡ ~ q’ and ‘~ q ⊃ ~ p’ are :
In the ranking of a competitive examination Vishal was above Vijay but below Shyam. Mohan was above Shyam but below Rohan. Vijay was between Vishal and Ashok. Who is third from the top ?
Ragini facing East walks 10 meter, then she turns to her left and walks 12 meter. Then she turns to her right in $45^o$ and walks 15 meter. Then, how much distance she has walked from the starting point and which direction is she facing now ?
In the Wason selection task for propositional reasoning, ‘participants develop a general idea of the rule, then construct examples that follow the rule’ is referred to as :
Important Questions from Deductive - Teaching
Match List I and List II and select the correct answer from the codes given below :
List I List II (a) ~ (p ∨ ~ p) (1) Identity (b) ~ (p • ~ p) (2) Contingency (c) ~ (p ⊃ q) (3) Tautology (d) p ⊃ p (4) Contradiction Codes :
(a) (b) (c) (d)
Which of the following is not the characteristics of an effective decision procedure ?
Correct formulation of the Rule U.I. (Universal Instantiation) is ........... .
Law of contradiction states that :
Characteristics of an Axiomatic systems are ................. .
(1) Consistency
(2) Completeness
(3) Independence
(4) Contingent
