Logical deduction – syllogism with set relations: “Only good singers are invited to the conference, and no one without a sweet voice qualifies as a good singer.” Based on these premises, determine which conclusions necessarily follow about invitees and singers lacking a sweet voice.

Given data

• Premise 1: Only good singers are invited to the conference. (Invited ⇒ Good Singer)
• Premise 2: No one without a sweet voice is a good singer. (Good Singer ⇒ Sweet Voice)
• Conclusion I: All invited singers have sweet voice.
• Conclusion II: Singers who do not have a sweet voice are not invited.

Concept/Approach (set-chain reasoning)
The premises create a transitive chain: Invited ⇒ Good Singer ⇒ Sweet Voice. Also, contrapositive reasoning applies: Not Sweet Voice ⇒ Not Good Singer ⇒ Not Invited.

Step-by-step deduction
1) From Premise 1: Invited ⇒ Good Singer.2) From Premise 2: Good Singer ⇒ Sweet Voice.3) Chain them: Invited ⇒ Sweet Voice. Thus, Conclusion I holds.4) Take contrapositive of step (2): Not Sweet Voice ⇒ Not Good Singer.5) Use Premise 1 contrapositive style: Not Good Singer ⇒ Not Invited (since only good singers are invited).6) Combine (4) and (5): Not Sweet Voice ⇒ Not Invited. Thus, Conclusion II holds.

Verification/Alternative
A Venn/arrow diagram Invited → Good → Sweet validates both conclusions immediately.

Common pitfalls

• Reversing the arrow (assuming Good Singer ⇒ Invited). The premise is 'only good singers are invited', not 'all good singers are invited'—but both conclusions rely only on Invited ⇒ Sweet and Not Sweet ⇒ Not Invited, which are valid.

Final Answer
Both I and II follow.