Implications

Step 1: Understand the given proportion.
We are given the proportion: This means that if both and are true, then must also be true.

Step 2: Find the inverse of the proportion.
The inverse of a conditional statement is given by: Thus, the inverse of is: Using De Morgan's law, becomes: So the inverse of the given proportion becomes:

Step 3: Check the options.
The inverse that we derived is , which matches option (B), , when written in a simplified form.

Step 4: Conclusion.
Thus, the inverse of the given proportion is , corresponding to option (B).

Step 1: Formula / Definition}

Step 2: Calculation / Simplification}
I: . If (even prime), even even. can be 2? No, sum>2. But (possible)
II: . Odd + odd = even. must be 2 (only even prime). not prime, but (odd+odd=odd? Wait: odd prime, odd even impossible since ) Never true.
III: . Product of two primes is composite (has factors 1,a,b,ab). Never prime. Never true.
IV: . (possible).
III is definitely never true. II is also never true. Check options: Only III is (C). But wait: II: (even prime), (possible). So II can be true.
Only III is never true.
Step 3: Final Answer