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Quiz about Vacuous Truth and Triangular Falsehood
Quiz about Vacuous Truth and Triangular Falsehood

Vacuous Truth and Triangular Falsehood Quiz


A statement is "vacuously true" if the premise is not true. For instance, "if pigs fly then I will speak to him again" remains true so long as pigs never fly. Another true statement is "if 3 is even then so is 5". Can you sort truth from falsehood?

A photo quiz by AdamM7. Estimated time: 2 mins.
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Author
AdamM7
Time
2 mins
Type
Photo Quiz
Quiz #
414,882
Updated
Feb 16 24
# Qns
10
Difficulty
Average
Avg Score
6 / 10
Plays
406
Last 3 plays: Guest 172 (4/10), cisley1972 (7/10), Guest 99 (7/10).
Author's Note: Consider a conditional "if [premise] then [conclusion]" statement. The statement is false if the premise is true and the conclusion is false; otherwise the statement is true.
Question 1 of 10
1. A freebie: If this picture shows a triangle then the triangle is red.

(This is vacuously true, so select "True".)


Question 2 of 10
2. If this picture shows a triangle then the triangle is red.


Question 3 of 10
3. If there is a triangle in this picture then every shape is colored red.


Question 4 of 10
4. If the answer to this question is "False", then the answer to this question is "True".


Question 5 of 10
5. All the questions in this quiz with three white circles have the answer "True".


Question 6 of 10
6. There are double the number of triangles in this picture than circles.


Question 7 of 10
7. If there are five "True" answers in this quiz, then there are five "False" answers.


Question 8 of 10
8. The earliest "False" answer in this quiz is matched to a picture of a red triangle.


Question 9 of 10
9. The latest question in this quiz with the answer "True" has an even question number.


Question 10 of 10
10. There are more triangles in the ten pictures in the quiz than "True" answers in the quiz.



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View Image Attributions for This Quiz

Most Recent Scores
Oct 30 2024 : Guest 172: 4/10
Oct 29 2024 : cisley1972: 7/10
Oct 28 2024 : Guest 99: 7/10
Oct 26 2024 : Guest 167: 4/10
Oct 24 2024 : Guest 68: 4/10
Oct 21 2024 : Guest 207: 8/10
Oct 18 2024 : Guest 108: 8/10
Oct 14 2024 : Guest 59: 6/10
Oct 10 2024 : Mitrayan: 9/10

Quiz Answer Key and Fun Facts
1. A freebie: If this picture shows a triangle then the triangle is red. (This is vacuously true, so select "True".)

Answer: True

The premise ("this picture shows a triangle") is false so the statement is vacuously true. It doesn't matter that the conclusion is false.
2. If this picture shows a triangle then the triangle is red.

Answer: False

The premise is true but the conclusion is false, making the statement untrue.

Of the four possibilities for an "if [premise] then [conclusion]" statement, a true premise and false conclusion is the only way that the statement is "False". In Boolean logic, this might be represented with a "truth table" of possible "True"/"False" values for the premise, conclusion and overall statement.
3. If there is a triangle in this picture then every shape is colored red.

Answer: True

The premise is false so the statement is vacuously true - we don't even need to read the conclusion (which happens to be true).
4. If the answer to this question is "False", then the answer to this question is "True".

Answer: True

If we selected "False" then the premise is true but the conclusion is false, making the statement false and the answer a contradiction. However, when we select "True", the premise is false, making the statement vacuously true.

It is not a paradox, as it is not the case that both choices ("True" and "False") lead to a contradiction - only "False" does.
5. All the questions in this quiz with three white circles have the answer "True".

Answer: True

Since no question contains three white circles, the statement is vacuously true. All of the zero questions that meet the premise (containing three white circles) meet the conclusion (answer "True").

If this question had three white circles in its picture, we would get an unusual choice: either click "True", making the statement true, or click "False", making the statement false. This is not a paradox as there is no contradiction, just ambiguity as to which answer is correct, but it would break the quiz.
6. There are double the number of triangles in this picture than circles.

Answer: False

Even though there are no circles, this is not phrased as a conditional that is vacuously true.

Instead, we count the number of circles - zero - and the number of triangles - two - and observe that double zero is not two.
7. If there are five "True" answers in this quiz, then there are five "False" answers.

Answer: True

We can answer this question without knowing whether there are five "True" answers or not. If there are five "True" answers then (given the ten total answers of either "True" or "False") that makes five "False" answers, so the statement is true. If there are not five "True" answers then the statement is vacuously true.

In fact it is necessary to answer this question before we know whether there are five "True" answers - which there turn out to be. Question 10 (and in turn question 9) rely on knowing that there are at least five "True" answers in the quiz, including this one.
8. The earliest "False" answer in this quiz is matched to a picture of a red triangle.

Answer: False

The premise refers to question 2, which has a "False" answer, but its picture is of a white triangle. A true premise and false conclusion makes the overall statement false.
9. The latest question in this quiz with the answer "True" has an even question number.

Answer: False

We have to answer question 10 first, as a "True" answer there would immediately make this statement true.

Question 10 has the answer "False" and the most recent true answer is to question 7. So, the last "True" answer is either question 7 or question 9 (if we select "True" here). Either way, the question number is odd, making this statement false (and the latest "True" answer match up with question 7).
10. There are more triangles in the ten pictures in the quiz than "True" answers in the quiz.

Answer: False

With ambiguity at this point over whether question 9 and 10 have the answer "True", we can say that there are five, six or seven "True" answers in the quiz. There are only four triangles, so we can be confident this answer is "False".

In turn this lets us answer question 9 as "False" and observe that the five "True" answers just barely exceed the four total triangles.
Source: Author AdamM7

This quiz was reviewed by FunTrivia editor Fifiona81 before going online.
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