Chapter 2.CR, Problem 21CR

To determine

a.

To classify:

Whether the statement “For all sets of A and B, either $\text{A}\subseteq \text{B or B}\subseteq \text{A}$” is true or false.

To determine

b.

To classify:

Whether the statement “The empty set is a proper subset of every set” is true or false.

To determine

c.

To classify:

Whether the statement “For all sets of A and B, if $\text{A}\sim \text{B}$, then A = B” is true or false.

To determine

d.,

To classify:

Whether the statement “The set {5, 10, 15, 20, …} is a finite set” is true or false.

To determine

e.

To classify:

Whether the statement “No set is equivalent to proper subset of itself” is true or false.

To determine

f.

To classify:

Whether the statement “If A is an infinite set and $\text{B}\subseteq \text{A}$, then B also is an infinite set” is true or false.

To determine

g.

To classify:

Whether the statement “For all finite sets A and B, if $\text{A}\cap \text{B}\ne \varnothing$, then $\text{n(A}\cup \text{B)}\ne \text{n(A)+n(B)}\text{.}$” is true or false.

To determine

h.

To classify:

Whether the statement “If A and B are sets such that $\text{A}\cap \text{B}\ne \varnothing$, then $\text{A=}\varnothing \text{ or B=}\varnothing$” is true or false.