# Common Mistakes on HW 9

A ⊆ B \equiv ∀ a ∈ A, a ∈ B. It does not mean '∀ b ∈ B, b ∈ A' or '∃ b ∈ B such that b ∈ A' or '∃ a ∈ A such that a ∈ B'. (mistakes on this did show up a few times in #20 and #21 of 4.4)

#27(b) of section 5.2: P(10,10) = 10! and P(10,0) = 1 (i.e. they are not the same, possible confusion of P(n,r) with C(n,r))

- #15(d) of section 5.2: the word 'exactly' was often ignored
#6 on section 5.3: the 2

^{5 was missed in a lot of the answers 4!*2}5 = 768 and 5!*2^5 = 3840 are acceptable answers (depending on whether the 5 rotations are counted as 1 way or 5 ways). Other answers are not acceptable.