NO 4 3 Determine whether the following have the same truth v

NO 4 3. Determine whether the following have the same truth values. (a) for all x(P(x) arrow Q(x)) and for all xP(x) -for all xQ(x). (b) for all T(P(r) V Q(r)) and for all xP(x) V for all xQ(x). (c) for all x(P(x) Cap Q(x)) and for all xP(x) cap for all xQ(x). s 4. Determine the truth values of the following statements. The universe under consideration is the set of all integers. (a ) nm ( m^2 + n^2 = 10) (b) for all nm(m^2 + n^2 = 10) ( c) for all nm(mn = 1)

Solution

(a) F

Let m²>10, there is no value of n for which m²+n²=10

(b) F

For n>10^0.5, there is no value of m exist for which m²+n²=10

(c) F

For n=0, there is no value of m for which mn=1, unless m=infinity which is not in the domain.