Elementary Logic by Robert Lover

Author:Robert Lover
Language: eng
Format: epub
Publisher: Springer London, London

(b)In order for (Pa ∨ Qa) ∧ ∀xRx to be true in I, both (Pa ∨ Qa) and ∀xRx must be true in I.

(c)In order for Pa ∨ Qa to be true in I, either Pa or Qa must be true in I.

(d)But Pa is false in I because V(a) = Jane, V(P) = {Jack, Jill}, and hence Jane is not an element of V(P).

(e)On the other hand, Qa is true in I since V(a) = Jane, V(Q) = {Jack, Jill Jane}, and therefore Jane is an element of V(Q).

(f)So Pa ∨ Qa is true in I.

(g)On the other hand, ∀xRx is false in I because if V is extended so Vx(x)= Dick we have an extension I of I to x in which Vx(x) ̃∈Vx(R).

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