Question $7$ Consider the following statements, where the domain of each variable is $R$ :

$(1)$ ForEvery $x$ ThereExists AND $(2x-y=1).$

$(2)$ ThereExists $x$ ForEvery $y(y0xy=1).$

$(3)$ ForEvery $x$ ForEvery $y$ ThereExists $z(x+y=2z).$

Select one of the following choices:

a$.(1)$ is False, and $(2)$ and $(3)$ are True

b$.(1)$ and $(3)$ are False, and $(2)$ is True

c$.(1)$ and $(2)$ are False, and $(3)$ is True

d$.(1)$ and $(2)$ are True, and $(3)$ is False

e$.$ None of the Given Choices