Are these statements true or false The universe of discourse

Are these statements true or false? The universe of discourse is the set of all people, and T(x, y) means \"x and y are twins.\" Explain how you determined your solution. Forall x not T(x, x) y T(y, y) x Forall y T(x, y) Forall x not y T(x, y) x not y T(x, y) Forall x not Forall y T(x, y)

Solution

Solution :

a. x ¬T(x, x)

True: For all people there is not a situation where x and x are twins.

b. y T(y, y)

False: There exists a y where y and y are twins.

c. x y T(x, y)

True: There exists an x that for all y\'s, x and y are twins.

d. x ¬y T(x, y)

False: For all x\'s there does not exist a y where x and y are twins.

e. x ¬y T(x, y)

True: There exists an x where there is not a y where x and y are twins.

f. x ¬y T(x, y)

False: For all x\'s and not for all y\'s, x and y are twins.