Question

Match the LIST-I with LIST-II. 

LIST-I	LIST-II
A. All human beings are mortal	I. \( (\exists x)(Hx \cdot Mx) \)
B. No human beings are mortal	II. \( (\exists x)(Hx \cdot \sim Mx) \)
C. Some human beings are mortal	III. \( (x)(Hx \supset Mx) \)
D. Some human beings are not mortal	IV. \( (x)(Hx \supset \sim Mx) \)

Choose the correct answer from the options given below.

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

Hint:

Universal statements use \((x)\), while particular statements use \((\exists x)\).

Answer 1

The Correct Option is A

Concept:
In predicate logic, universal propositions are represented with the universal quantifier, and particular propositions are represented with the existential quantifier. Here: \[ Hx = x \text{ is a human being} \] \[ Mx = x \text{ is mortal} \]

Step 1: Translate A.
\[ \text{All human beings are mortal} \] This means: \[ (x)(Hx \supset Mx) \] So: \[ A \rightarrow III \]

Step 2: Translate B.
\[ \text{No human beings are mortal} \] This means: \[ (x)(Hx \supset \sim Mx) \] So: \[ B \rightarrow IV \]

Step 3: Translate C.
\[ \text{Some human beings are mortal} \] This means: \[ (\exists x)(Hx \cdot Mx) \] So: \[ C \rightarrow I \]

Step 4: Translate D.
\[ \text{Some human beings are not mortal} \] This means: \[ (\exists x)(Hx \cdot \sim Mx) \] So: \[ D \rightarrow II \]

Step 5: Final matching.
The correct matching is: \[ A-III,\ B-IV,\ C-I,\ D-II \] Hence: \[ \boxed{\text{(A)}} \]