Deductive logic from conditional statements
Question
Let P, Q, R, S and T be five statements such that: I. If P is true, then both Q and S are true. II. If R and S are true, then T is false. Which of the following can be concluded ?
Select the correct answer using the code given below:
Options
1 only
2 only
Both 1 and 2
Neither 1 nor 2
Explanation
Translate the statements into formal symbolic logic notation :
Evaluate Conclusion 1: Assume T is true (T)[cite: 4411, 4473]. By the law of contraposition applied to Premise II, \neg(\neg T) \implies \neg(R \land S) \implies \neg R \lor \neg S. Since T is true, at least one of ⟨MATH⟩R⟨/MATH⟩ or ⟨MATH⟩S⟨/MATH⟩ must be false.
Therefore, if T is true, either R is false or P is false. This matches Conclusion 1 precisely. Valid [cite: 4415, 4484].
Evaluate Conclusion 2: Q \implies P[cite: 4413, 4474]. This represents the formal fallacy of affirming the consequent. Knowing the consequence (Q) is true does not validate that the initial condition (P) triggered it. Invalid[cite: 4415, 4484].
Answer: (a).
Question details
Year
2023
Paper
CSAT
Question
Q78
Section
Logical & Analytical Reasoning
Sub-topic
Syllogism
Type
Inequality logic
Difficulty
Medium
Source hint
Logical deduction
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