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Exercise 2.2
1. |
Which of the following are truth functors? Where the expression is a truth-functor, what is its truth-table? Where it is not a truth-functor what is its partial truth-table? (A partial truth-table is a truth-table in which some rows have a "?" in them; in these cases, think of pairs of examples to show that sometimes the resulting sentence will be true in these cases and sometimes the resulting sentence will be false.)
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(i)
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j or y or both. | |
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(ii)
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It is true that j | |
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(iii)
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It is a necessary truth that j | |
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(iv)
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It could have been the case that j | |
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(v)
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j, but not because y | |
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(vi)
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It is true that j or it isn't | |
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(vii)
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j, but grass is not green | |
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(viii)
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j, whether or not grass is green | |
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(ix)
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Everyone knows that it is true that j or it isn't | |
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