1) Determine whether these statements are true or false. Please explain why so I can understand...

1) Determine whether these statements are true or false. Please explain why so I can understand where the answers came from

a) ∅ ∈ {∅}

b) ∅ ∈ {∅, {∅}}

c) {∅} ∈ {∅}

d) {∅} ∈ {{∅}}

e) {∅} ⊂ {∅, {∅}}

f ) {{∅}} ⊂ {∅, {∅}}

g) {{∅}} ⊂ {{∅}, {∅}}

2) Let A = {a, b, c}, B = {x, y}, and C = {0, 1}. Find

a) A x B x C

d) B x B x B

3) Show that if A and B are sets, then

b) (A ⊕ B) ⊕ B = A. (prove every step! you may use the fact that symmetric difference of sets is associative)

Expert Solution

Colby Messinger answered 2 years ago

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