Logic

Syllogistic Logic: Level 2 Challenges

Which of the statements X, Y, Z below must be true?

Y: Some plonks are plunks.
Z: Some plinks are not plunks.

We are given the two statements above. Which of the following conclusions must be true?

(1): All houses are pens.

(2): Some houses are pens.

Assume that the set of pens is non-empty.

Given below are three statements followed by three conclusions. Take the three statements to be true even if they vary from commonly known facts. Read the statements and decide which conclusions follow logically from the statements.

Statements:
1. All actors are musicians.
2. No musician is a singer.
3. Some singers are dancers.

Conclusions:
1. Some actors are singers.
2. Some dancers are actors.
3. No actor is a singer.

a) Only conclusion 1 follows.
b) Only conclusion 2 follows.
c) Only conclusion 3 follows.
d) At least 2 of the conclusions follows.

What conclusion follows from the statements given below?

$(1)$ Nobody who really appreciates Beethoven fails to keep silent while the Moonlight Sonata is being played.

$(2)$ Guinea-pigs are hopelessly ignorant of music.

$(3)$ No one who is hopelessly ignorant of music ever keeps silent while the Moonlight Sonata is being played.

This problem is from Lewis Carrol (Yes, Alice in Wonderland!), who was an accomplished author as well as a mathematician specialising in logic.

This problem is the part of my set Is This What You Call Logic?!

Anything magical is dangerous.

All dragons are sparkly.

Given the above two statements are true, what would (if true) make the statement "All dragons are dangerous" true?

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