Find if statements are T or F and give explanation?

Am I on the right tracK

$\displaystyle (\forall x \in R) (x >=$ -5)

False. Not all real numbers are greater than or equal to -5. An example would be x=-4

$\displaystyle (\exists z \in R) (z < 1)$

True. There is, at least one, real number z that is less than one. An example: z = -1

$\displaystyle (\exists m \in R) (\forall x \in R) (xm = m)$

False. For example, let m=8 and x = -1. -8 != 8.

$\displaystyle (\exists t \in R) (\forall x \in R) (t < x )$

False. Let x = 1 and t=10