Answer
a. True, Z+⊆Q since all positive integers can be stated as x/1, which is a rational number.
b. False, R-⊈Q since there are negative real numbers that are not rational, such as -√2 and -π.
c. False, Q⊈Z since there are rational numbers that are not integers, such as 5/8.
d. False, Z- ⋃ Z+ ≠ Z since 0 ϵ Z but 0∉Z- and 0∉Z+ since 0 is neither positive or negative.
e. True, since Z- ⋂ Z+ have no common elements.
f. True, since Q ⊆R
g. True, since Z⊆Q
h. True, since Z+ ⊆R
i. False, since Q⊈Z
Work Step by Step
a. True, Z+⊆Q since all positive integers can be stated as x/1, which is a rational number.
b. False, R-⊈Q since there are negative real numbers that are not rational, such as -√2 and -π.
c. False, Q⊈Z since there are rational numbers that are not integers, such as 5/8.
d. False, Z- ⋃ Z+ ≠ Z since 0 ϵ Z but 0∉Z- and 0∉Z+ since 0 is neither positive or negative.
e. True, since Z- ⋂ Z+ have no common elements.
f. True, since Q ⊆R
g. True, since Z⊆Q
h. True, since Z+ ⊆R
i. False, since Q⊈Z