SOLUTIONS - UNIONS, INTERSECTIONS AND COMPLEMENTS

QUESTION 1

If LaTeX: U=\left\{m,\:o,\:n,\:a,\:r,\:c,\:h\right\}, LaTeX: A=\left\{m,\:a,\:r,\:c,\:h\right\} and LaTeX: B=\left\{c,\:o,\:r,\:n\right\} determine

  • LaTeX: A\cup BLaTeX: =\left\{m,\:a,\:r,\:c,\:h,\:o,\:n\right\}
  • LaTeX: A\cap BLaTeX: =\left\{r,\:c\right\}
  • LaTeX: A'LaTeX: =\left\{o,\:n\right\}
  • LaTeX: B'LaTeX: =\left\{m\:,\:a,\:h\right\}
  • LaTeX: \left(A\cup B\right)'LaTeX: =\left\{\right\}
  • LaTeX: \left(A\cap B\right)'LaTeX: =\left\{m,\:o,\:n,\:a,\:h\right\}
  • LaTeX: A\cup B'LaTeX: =\left\{m,\:a,\:r,\:c,\:h\right\}
  • LaTeX: A\cap B'LaTeX: =\left\{m,\:a,\:h\right\}

QUESTION 2

If LaTeX: U=\left\{a,\:f,\:,t,\:e,\:r,\:s,\:h,\:o,\:c,\:k\right\}, LaTeX: A=\left\{h,\:e,\:a,\:r,\:t\right\} and LaTeX: B=\left\{c,\:h,\:o,\:k,\:e\right\} determine

  • LaTeX: A\cup BLaTeX: =\left\{h,\:e,\:a,\:r,\:t,\:c,\:o,\:k\right\}
  • LaTeX: A\cap BLaTeX: =\left\{h,\:e\right\}
  • LaTeX: A'LaTeX: =\left\{f,\:s,\:o,\:c,\:k\right\}
  • LaTeX: B'LaTeX: =\left\{a,\:f,\:t,\:r,\:s\right\}
  • LaTeX: \left(A\cup B\right)'LaTeX: =\left\{f,\:s\right\}
  • LaTeX: \left(A\cap B\right)'LaTeX: =\left\{a,\:f,\:t,\:r,\:s,\:o,\:c,\:k\right\}
  • LaTeX: A\cup B'LaTeX: =\left\{h,\:e,\:a,\:r,\:t,\:f,\:s\right\}
  • LaTeX: A\cap B'LaTeX: =\left\{a,\:r,\:t\right\}

QUESTION 3

If LaTeX: U=\left\{r,\:e,\:d,\:u,\:c,\:t,\:i,\:o,\:n,\:s\right\}, LaTeX: A=\left\{n,\:o,\:i,\:s,\:e\right\} and LaTeX: B=\left\{s,\:u,\:c,\:t,\:i,\:o,\:n\right\} determine

  • LaTeX: A\cup BLaTeX: =\left\{n,\:o,\:i,\:s,\:e,\:u,\:c,\:t\right\}
  • LaTeX: A\cap BLaTeX: =\left\{n,\:o,\:i,\:s\right\}
  • LaTeX: A'LaTeX: =\left\{r,\:d,\:u,\:c,\:t\right\}
  • LaTeX: B'LaTeX: =\left\{r,\:e,\:d\right\}
  • LaTeX: \left(A\cup B\right)'LaTeX: =\left\{r,\:d\right\}
  • LaTeX: \left(A\cap B\right)'LaTeX: =\left\{r,\:e,\:d,\:u,\:c,\:t\right\}
  • LaTeX: A\cup B'LaTeX: =\left\{n,\:o,\:i,\:s,\:e,\:r,\:d\right\}
  • LaTeX: A\cap B'LaTeX: =\left\{e\right\}