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Let L(x,y) be the statement "x lives with y", where the domain for both x and y is all people.

use the quantifiers (∀,∃) to express the following statement

(1) Someone lives with exactly two people.

(2) There is somebody who lives with somebody.

(3) There is somebody whom no one lives with.

PS: I think "There is somebody who lives with somebody" is same with "somebody live with somebody". ∃x ∃y L(x,y), Is it right?

Daniel Zhang
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1 Answers1

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  1. There is somebody who lives with exactly two people: $\exists(x)[\exists!(a,b)[Lxa \wedge Lxb]]$
  2. There is somebody who lives with somebody: $\exists(x,y)[Lxy]$
  3. There is somebody whom no one lives with: $\exists(x)[\not\exists(y)[Lxy]]$