Question

Match the LIST-I with LIST-II

LIST-I (Rules of Deduction)	LIST-II (Examples)
A. Modus Ponens	III. P $\Rightarrow$ Q, P, Therefore, Q
B. Modus Tollens	I. P $\Rightarrow$ Q, $\neg$ Q, Therefore, $\neg$ P
C. Hypothetical Syllogism	IV. P $\Rightarrow$ Q, Q $\Rightarrow$ R, Therefore, P $\Rightarrow$ R
D. Disjunctive Syllogism	II. P $\vee$ Q, $\neg$ P, Therefore, Q

Choose the correct answer from the options given below:

• A. A- III, B- I, C- II, D- IV
• B. A- II, B- IV, C- I, D- III
• C. A- II, B- I, C- III, D- IV
• D. A- III, B- II, C- IV, D- I

Hint:

In logical reasoning, understanding the rules of deduction helps in analyzing and constructing valid arguments using premises and conclusions.

Answer 1

The Correct Option is D

Step 1: Analyzing the rules of deduction.
- Modus Ponens (A): If P $\Rightarrow$ Q is true and P is true, then Q must be true. This matches with III. - Modus Tollens (B): If P $\Rightarrow$ Q is true and $\neg$ Q is true, then $\neg$ P must be true. This matches with I. - Hypothetical Syllogism (C): If P $\Rightarrow$ Q and Q $\Rightarrow$ R are true, then P $\Rightarrow$ R must be true. This matches with II. - Disjunctive Syllogism (D): If P $\vee$ Q is true and $\neg$ P is true, then Q must be true. This matches with IV.
Step 2: Conclusion. The correct answer is Option 4.
Final Answer: \[ \boxed{\text{The correct answer is 4. A - III, B - I, C - II, D - IV.}} \]