Each of the possible eight outcomes of a random experiment i

Each of the possible eight outcomes of a random experiment is equally likely. Thesample space is {a, b, c, d, e, f, g, h}. Let A denote the event {a, b, c, e}, let B denote theevent {c, d, e} and let C denote the event {f,g,h}. Determine the following: (Three events areshown on the Venn diagram in the following figure. You can work on the diagram – optional)

(a)A ’
(b) (A? B)? (A ? B ? )
(c) ( A ? B) ? C
(d) (B ? C) \'
(e) (A?B) ? ? C

Solution

Thesample space is {a, b, c, d, e, f, g, h}. Let A denote the event {a, b, c, e}, let B denote theevent {c, d, e} and let C denote the event {f,g,h}.

a)A\'

U={a, b, c, d, e, f, g, h}, A={a, b, c, e},B={c, d, e},C={f,g,h}.

A\'={d,f,g,h}

(b) (A B) (A B )

AnB={c,e}

B\'={a,b,f,g,h}

AnB\'={a,b}

(A B) (A B )={a,b,c,e}

(c) ( A B) C

AnB={c,e}

( A B) C={c,e,f,g,h}

(d) (B C) \'

BuC={c,d,e,f,g,h}

(B C) \' ={a,b}

(e) (AB) C

AnB={c,e}

(AB) ={a,b,d,f,g,h}

(AB) C={a,b,d,f,g,h}