Russ P. answered • 10/14/14

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Rose,

To not get lost, I recommend writing out the sets and their complement sets beforehand, then addressing the questions.

The Venn world set U = {a, b, c, d, e} of cardinal#5 i.e, it has 5 members

X = {a, c, d} so X' = {b, e}

Y = {b, d} so Y' = {a, c, e}

Z = {a, e} so Z' = {b, c, d}

(a) (X' U Y)' U Z

= ({b,e} U {b,d})' U {a,e}

= ( {b,d,e})' U {a,e}

= {a, c} U {a, e}

= {a, c, e} & Cardinal# = 3

(b) X U (Y' n Z')

= {a,c,d} U ({a,c,e} n {b,c,d})

= {a,c,d} U ({c})

= {a, c, d} & Cardinal# = 3

(c) X - Z'

= {a,c,d} - {b,c,d} that is remove the members of Z'

= {a} & Cardinal# = 1