Assuming that "Since all atheists are opponents of monotheism, some atheists are not opponents of monotheism" has a true premise, use the traditional square of opposition to calculate the truth value of its conclusion

a) true
b) false
c) undetermined


Traditional square of opposition is an arrangement of lines that illustrates logically necessary relations among the four kinds of categorical propositions

image

Diagram is supplemented with the following explanations:

Two propositions are contradictory iff they cannot both be true and they cannot both be false.
Two propositions are contraries iff they cannot both be true but can both be false.
Two propositions are subcontraries iff they cannot both be false but can both be true.
A proposition is a subaltern of another iff it must be true if its superaltern is true, and the superaltern must be false if the subaltern is false.

Answering your question it is false because two propositions which is "atheists are/not opponents of monotheism" are contradictory. if they cannot both be true and they cannot both be false where the statement says it is true.

Philosophy & Belief

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