Question

Consider the sets. A= {distinct letters in the word pipe}B= {13}C= {p, i, e}D= {5 + 1}E= {six}F= {6}
(a) What is the cardinality of each set?|A|=|B|=|C|=|D|=|E|=|F|=

(b) Which of the sets are equivalent?

A ↔ C ↔ B ↔ D ↔ E ↔ F

A ↔ C ↔ D; E ↔ F

A ↔ C; B ↔ D ↔ E ↔ F

A ↔ C; D ↔ E ↔ F

A ↔ B; C ↔ D; E ↔ F

(c) Which of the given sets are equal?

A = C; B = D = E = F

A = C = D; E = F

C = E = F

A = C; D = E = F

A = C = D = E = F

Answer 1

disclaimer: I haven't officially learned set theory but I think I know enough to solve this.

a) cardinality is the # of distinct elements in a set. for example, set A is {p,i,p,e} which has 3 distinct elements (p, i, e, not including the repeated p). repeat this process for the other sets

b) equivalent sets have equal cardinality. so from part a) simply identify which sets have the same cardinality as each other.

c) equal sets have the exact same elements.