Using the Venn diagram, find 𝑌
union 𝑋 bar.
Let’s begin by defining some of the
notation in this question. The U-shaped symbol between 𝑌 and
𝑋 bar means the union. In probability, this means or. We need to find the set of values
that are in 𝑌 or in 𝑋 bar. The notation 𝑋 bar means the
complement of 𝑋. This is the set of all values not
We can see from the Venn diagram
that set 𝑈 is all the numbers shown. This is the integer values from one
to nine. The set of values contained in
circle 𝑌 are one, two, six, and nine. The set of values in circle 𝑋 are
one, three, and six. This means that the complement of
𝑋 will be all the values except these. The numbers that are not in set 𝑋
are two, four, five, seven, eight, and nine.
We recall that we need to find the
values that are in set 𝑌 or in set 𝑋 bar. The numbers two and nine appear in
both of these sets, but we do not need to write this number twice. The set of numbers contained within
the union of 𝑌 and 𝑋 bar are one, two, four, five, six, seven, eight, and
nine. In fact, the only number that is
not in this union is three. This is because it appears in set
𝑋, but not in set 𝑌. As we want all the values that are
either in set 𝑌 or not in set 𝑋, we do not include the three.