Question

5. (12 points) For each following pair of sets, determine whether they are disjoint, equal, proper subset/superset, or none of the above. Prove your answers. (a) {x in mathbb{Z} mid x^2 = x} and {x in mathbb{R} mid x^2 = x}. (b) {x in mathbb{R} mid lfloor x floor = x} and mathbb{Q}. (c) {x in mathbb{R} mid x^2 < x} and {x in mathbb{R} mid x otin mathbb{Q}}. (d) {x in mathbb{Z}^+ mid x ext{ is prime}} and {-1, 0, 1}. Note: use the definition of prime as giving in Definition 1 of Section 4.3 ""An integer $p$ greater than 1 is prime iff the only positive factors of $p$ are 1 and $p"".

          5. (12 points) For each following pair of sets, determine whether they are disjoint, equal,
proper subset/superset, or none of the above. Prove your answers.
(a) {x in mathbb{Z} mid x^2 = x} and {x in mathbb{R} mid x^2 = x}.
(b) {x in mathbb{R} mid lfloor x 
floor = x} and mathbb{Q}.
(c) {x in mathbb{R} mid x^2 < x} and {x in mathbb{R} mid x 
otin mathbb{Q}}.
(d) {x in mathbb{Z}^+ mid x 	ext{ is prime}} and {-1, 0, 1}.
Note: use the definition of prime as giving in Definition 1 of Section 4.3 ""An integer $p$
greater than 1 is prime iff the only positive factors of $p$ are 1 and $p"".

5. (12 points) For each following pair of sets, determine whether they are disjoint, equal,
proper subset/superset, or none of the above. Prove your answers.
(a) x in mathbbZ mid x^2 = x and x in mathbbR mid x^2 = x.
(b) x in mathbbR mid lfloor x
floor = x and mathbbQ.
(c) x in mathbbR mid x^2 < x and x in mathbbR mid x
otin mathbbQ.
(d) x in mathbbZ^+ mid x ext is prime and -1, 0, 1.
Note: use the definition of prime as giving in Definition 1 of Section 4.3 ""An integer p
greater than 1 is prime iff the only positive factors of p are 1 and p"".

Added by Angela R.

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