Discrete Math Question How does the order of the existential and universal quant

Question

Discrete Math Question

How does the order of the existential and universal quantifier changes the meaning of a sentence?

I just do not understand how are these two different, because in either case if the first predicate is false, the result of True according to the conditional truth table.

Could somebody please explain this to me in the simplest terms and with a lot of details?

Examples: English Quantifications Be careful to scope quantified variables appropriately "Everyone who is the parent of someone laughs at puns." Let L(x) be laughs at puns" Let POx,y be "x is the parent of L(x) Note: This means someone who isn't a parent might or might not laugh at puns, which is what we'd want! Warning This is different than Vx3y [POx,y) L(x)]! Why? The latter is much weaker! It just says that for each person we can find someone (could be that same person!) that makes the implication true. Since someone isn't a parent of themselves, this is trivially true without being able to claim anything about whether anybody laughs at puns!

Explanation / Answer

The first one says that for any given person x,if there another person y,who is child of y (P(X,Y) then he would laugh at puns.

where as the latter says given any person x, we can definitely find at least his one child y of x so that he be be seen as laughing on puns.

This is false in case a person x is not a parent then we cant find y.but the statement says we can find his child y so that he can be seen as laughing at puns.

Also , for the sake of calling latter true we cant club y as x because a person cant be parent of himself/herself.

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.