If the proposition ‘Houses are not bricks’ is taken to be False then which of the following propositions can be True?
(a) All houses are bricks
(b) No house is brick
(c) Some houses are bricks
(d) Some houses are not bricks
Select the correct answer from the options given below:
(c) only
Read 'Houses are not bricks' as the universal negative (E-type): 'No houses are bricks'. We are told this E proposition is False, and we must find which propositions can then be true.
On the square of opposition the contradictory of E is the particular affirmative (I-type): 'Some houses are bricks'. Contradictories always have opposite truth-values, so if E is False, its contradictory I must be True. Hence 'Some houses are bricks' is definitely true.
Now test the others. 'All houses are bricks' (A-type) is the contrary of E; when E is false, the contrary is undetermined — it may be true or false, so it cannot be asserted as true. 'No house is brick' is just E itself restated, which is given as false. 'Some houses are not bricks' (O-type) is the subaltern of E; when the universal E is false, its subaltern O is undetermined and cannot be guaranteed true. Therefore only 'Some houses are bricks' can be taken as true.
Correct answer: (c) only
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Important Questions from Classical Square of Opposition
Which of the following statements are so related that they can not both be true but could both be false?
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Choose the correct answer from the options given below:
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Which of the following statements are contradictory to each other?
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