Discrete Mathematics with Applications 4th Edition Chapter 6 - Set Theory - Exercise Set 6.1 - Page 350 16

Answer

A = {a, b, c} B = {b, c, d} C = {b, c, e} a. A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) A ∪ (B ∩ C) = {a, b, c} ⋃ ({b, c, d} ⋂ {b, c, e}) = {a, b, c} ⋃ {b, c} = {a, b, c} (A ∪ B) ∩ C = ({a, b, c} ⋃ {b, c, d}) ⋂ {b, c, e}) = {a, b, c, d} ⋂ {b, c, e} = {b, c} (A ∪ B) ∩ (A ∪ C) = ({a, b, c} ⋃ {b, c, d}) ⋂ ({a, b, c} ⋃ {b, c, e}) = {a, b, c, d} ⋂ {a, b, c, e} = {a, b, c} b. A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) A ∩ (B ∪ C) = {a, b, c} ⋂ ({b, c, d} ⋃ {b, c, e}) = {a, b, c} ⋂ {b, c, d, e} = {b, c} (A ∩ B) ∪ C = ({a, b, c} ⋂ {b, c, d}) ⋃ {b, c, e} = {b, c} ⋃ {b, c, e} = {b, c, e} (A ∩ B) ∪ (A ∩ C) = ({a, b, c} ⋂ {b, c, d}) ⋃ ({a, b, c} ⋂ {b, c, e}) = {b, c} ⋃ {b, c} = {b, c} c. No, these sets are not equal. (A − B) – C = ({a, b, c} - {b, c, d}) - {b, c, e} = {a} – {b, c, e} = {a} A − (B − C) = {a, b, c} – ({b, c, d} - {b, c, e}) = {a, b, c} – {d} = {a, b, c}

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