Logic

Logic is the study of reasoning and valid inference. It involves analyzing statements, arguments, and deductive processes. Questions may include solving logic puzzles, evaluating the truth of compound statements, using truth tables, and identifying logical fallacies.

• Question

  When it rains, Alice always drinks tea. Alice is currently drinking tea. Does it necessarily mean it is raining now?

  Topics:

  Logic -> Reasoning / Logic

• Question

  On the circle, there are blue and red points. It is allowed to add a red point and change the colors of its neighboring points or remove a red point and change the colors of its neighboring points (it is not allowed to leave fewer than 2 points on the circle). Prove that it is impossible to move, using only these operations, from a circle with two red points to a circle with two blue points.
  K. Kaznvosky

  Topics:

  Combinatorics -> Combinatorial Geometry Combinatorics -> Invariants Algebra Logic -> Reasoning / Logic Number Theory -> Division -> Parity (Even/Odd) Set Theory Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures Combinatorics -> Colorings -> Chessboard Coloring
  Sources:
  • Tournament of Towns, 1979-1980, Main, Spring Question 1

• Question

  Alice eats ice cream only when it is not raining. It is not raining now. Is Alice necessarily eating ice cream right now?

  Topics:

  Logic -> Reasoning / Logic

• Question

  Alice has three friends – Edith, Rose, and Mary. When Alice is sick, at least one of her friends comes to visit. Alice is sick, and Edith comes to visit her. Is it possible that Rose and Mary also came?

  Topics:

  Logic -> Reasoning / Logic

• Question

  When Rosa and Edith come to visit Alice, Alice's mother bakes a cake. Edith came to visit Alice today. Is Alice's mother necessarily going to bake a cake? Is Alice's mother necessarily not going to bake a cake?

  Topics:

  Logic -> Reasoning / Logic

• Question

  When it rains, Rosa always takes an umbrella with her and wears a coat. Today, Rosa wore a coat and took an umbrella with her. Is it necessarily the case that it is raining today?
  Topics:

  Logic -> Reasoning / Logic

• Question

  When there is snow and a strong wind, Alice doesn't meet her friends. Today there is snow. Is it possible that Alice meets her friends today?

  Topics:

  Logic -> Reasoning / Logic

• Question

  A disheveled soldier named Shlomi flees when he sees the regimental sergeant major (RSM) or the base commander. Shlomi is walking across the plaza and sees the base commander and the RSM walking together. Does he flee?

  Topics:

  Logic -> Reasoning / Logic

• Question

  When it's dark outside and there are no buses, Yossi and Danny always hang out together. Currently, there are no buses, and Yossi is walking alone to the park. Is it true that it is daytime now?

  Topics:

  Logic -> Reasoning / Logic Proof and Example -> Proof by Contradiction

• Jack the Cat

  My cat Jack purrs when he is happy and sitting in a warm place. Currently, Jack is cold.

  A. Is it possible that he is purring now?

  B. Is it possible that he is happy now?

  Topics:

  Logic -> Reasoning / Logic