A Hypothetical Quantifier in Predicate Logic

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My answer for this question is...

S=<{e1,e2,e3,...e10},I} I(linguist)={e1,e2,e3,...e10} I(married)={e1, e2,... e7}

I meant that there are 10 people, and 7 people out of 10 are linguists.To do this, I wanted to prove that "less than 60% of linguists are married". And, I wanted to prove that " Qx(linguist(x)∧married(x)) " is true.

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(A) For the domain $S$ with 10 elements, we can use:

$I(linguist) = \{ e_1,e_2,e_3 \}$ and $I(married) = \{ e_1,e_2 \}$.

In this way, we have that 2 on 3 linguists are married: $\dfrac 2 3 = 0.66$ and 66% > 60%.

Thus, (1a) is false.

At the same time, we have that only 2 elements of the domain $S$ are both linguists and married: $\dfrac 2 {10} = 0.2$ and 20% < 60%.

Thus, (1b) is true, because less than 60% of the elements of the domain $S$ are linguists and married.


(B) Now we want that (2a): "Less than 60% of the linguists are married" comes out true.

This is quite straightforward: it is enough to choose sets $I(linguist)$ and $I(married)$ in the ratio $2 : 1$.

But we want also that (2b): "$Qx \ (\text {linguist} (x) \to \text {married} (x))$ is false.

This means that we want that at least 60% of the entities in $S$ make the formula $\text {linguist} (x) \to \text {married} (x)$ true.

In conclusion, we can set: $I(linguist) = \{ e_1,e_2 \}$ and $I(married) = \{ e_1 \}$.

We have that 1 on 2 linguist is married: $\dfrac 1 2 = 0.5$ and 50% < 60%. Thus, (2a) is true.

At the same time, for every $e_i, i=3,\ldots,10$ we have that $\text {linguist} (e_i) \to \text {married} (e_i)$ is true.

Thus, 80% of the total population of $S$ satisfy the formula $\text {linguist} (x) \to \text {married} (x)$, and his means that "$Qx \ (\text {linguist} (x) \to \text {married} (x))$ is false.