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Using the truth table for the predicate $P$ over the domain $D=\{a,b,c\}$, where the first argument is the row of our truth table and the second is the column. For example, $P(b,c) = F$, whereas $P(c,b) = T$.

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Evaluate the truth values of the following predicate logic statement.

$$\exists x \forall y, P(y,x)$$

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  • $\begingroup$ What exactly is the difficulty with this? Try to express the statement in English. $\endgroup$ – Graham Kemp Mar 4 at 2:02
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Edit: Putting your statement into words: "exists a column such that its intersection with all rows is True". No column meets the condition, so the statement is False.

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