Logic Worksheet With Answers Page 20
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22An Euler diagram is a technique for determining the validity of arguments whose premises
contain the words all, some, and no.
Euler Diagrams and Arguments:
1. Make an Euler diagram for the first premise.
2. Make an Euler diagram for the second premise on top of the one for the first premise.
3. The argument is valid if and only if every possible diagram illustrates the conclusion of
the argument. If there is even one possible diagram that contradicts the conclusion, this
indicates that the conclusion is not true in every case, so the argument is invalid.
Ex:
Premise 1:
All students who arrive late cannot take the test.
Premise 2:
All students who cannot take the test are ineligible for a passing grade.
Conclusion:
Therefore, all students who arrive late are ineligible for a passing grade.
Ineligible for a passing grade
Cannot take test
Cannot take test
Since there is only one possible diagram, and it illustrates the argument’s conclusion the
argument is valid.
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