The compound statement A-> (A->B) is false, then the truth values of A, B are respectively _________a.T, Fb.F, Fc.F, Td.T, T
Question
The compound statement A -> (A -> B) is false, then the truth values of A, B are respectively _________
- a. T
- b. F
- c. F
- d. T
- T
Solution
The compound statement A-> (A->B) is a conditional statement, which is only false when the first part (antecedent) is true and the second part (consequent) is false.
Let's break it down:
-
A->B is the consequent of the main statement. For this to be false, A must be true and B must be false.
-
Now, considering the main statement A-> (A->B), for this to be false, A must be true (which we have already established) and (A->B) must be false (which we have also established).
So, the truth values of A and B that make the compound statement false are A = True and B = False.
Therefore, the answer is a. T, F.
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