PTA Logic Puzzles 1 — Questions and Answers
Question 1: In a logic puzzle, if A is taller than B and B is taller than C, what can you conclude?
- A is taller than C (Correct answer)
- C is taller than A
- They are all the same height
- No conclusion can be drawn
Correct answer: A is taller than C
Transitive property: if A > B and B > C, then A > C.
Question 2: What is a syllogism?
- A logical argument with two premises leading to a conclusion (Correct answer)
- A type of math problem
- A grammar rule
- A reading strategy
Correct answer: A logical argument with two premises leading to a conclusion
A syllogism uses deductive reasoning: "All dogs are animals. Rex is a dog. Therefore Rex is an animal."
Question 3: If all roses are flowers and some flowers are red, can we conclude all roses are red?
- No — we only know roses are flowers and some flowers are red; roses may or may not be red (Correct answer)
- Yes, all roses must be red
- Only garden roses are red
- Red is not a real color for flowers
Correct answer: No — we only know roses are flowers and some flowers are red; roses may or may not be red
This is a logical fallacy. The fact that some flowers are red does not mean all flowers (including roses) are red.
Question 4: What is a Venn diagram used for in logic?
- To visually represent relationships between sets and identify overlapping categories (Correct answer)
- To plot mathematical functions
- To diagram sentences
- To map geographical regions
Correct answer: To visually represent relationships between sets and identify overlapping categories
Venn diagrams use overlapping circles to show relationships between groups, making it easy to see what items belong to multiple categories.
Question 5: In a truth table, what value does "A AND B" have when A is true and B is false?
- False — AND requires both conditions to be true (Correct answer)
- True
- Sometimes true
- Undefined
Correct answer: False — AND requires both conditions to be true
The AND operator requires both inputs to be true for the output to be true. If either is false, the result is false.
Question 6: What is a contrapositive?
- If the statement "if A then B" is true, the contrapositive "if not B then not A" is also true (Correct answer)
- The opposite of a statement
- A type of hypothesis
- A negative assumption
Correct answer: If the statement "if A then B" is true, the contrapositive "if not B then not A" is also true
The contrapositive reverses and negates a conditional: "If it rains, the ground is wet" becomes "If the ground is not wet, it did not rain."
PTA Logic Puzzles 1
In a logic puzzle, if A is taller than B and B is taller than C, what can you conclude?