Ven diagram

Question

Given: U={a,b,c,d,e}; X={a,c,d}; Y={b,d} and Z={a,e} Find the following:

a) (X’ ∪ Y)’ ∪ Z & its Cardinal# (n)

b) X ∪ (Y’ ∩ Z’) & its Cardinal# (n)

c) X – Z’ & its Cardinal# (n)

Answer 1

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