Take the statements below to be true, even if they differ from known facts. Which of the conclusions follow logically from them?
Statements:
1. No glove is a scarf.
2. No scarf is a sock.
Conclusions:
I. All gloves being socks is a possibility.
II. Some socks are not scarves.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Both conclusions I and II follow
A “possibility” conclusion follows if it is true in at least one diagram that fits the statements; an ordinary conclusion must be true in every such diagram.
“No glove is a scarf”: the circles of gloves and scarves do not touch
“No scarf is a sock”: the circles of scarves and socks do not touch; nothing is said about gloves and socks
Conclusion I: All gloves being socks is a possibility. — Follows. Nothing stops the gloves lying inside the socks: the diagram fits both statements and in it all gloves are socks.
Conclusion II: Some socks are not scarves. — Follows. No scarf is a sock, so no sock is a scarf; there are socks, so some socks are not scarves.