Question

Given the following sets:

A = {a, b, c, d, e, f, g, h, i, j}
B = {d, p, q, z}
C = {v, w, x, y, z}
Find: n(BUC)
Do not list the set; just state its cardinality.

Answer 1

The union of B and C is

B U C = {d, p, q, v, w, x, y, z}

and n(B U C) = 8.

You can also use the inclusion/exclusion principle. Notice that B and C share only one common element (z). Then according to the principle,

n(B U C) = n(B) + n(C) - n(B ∩ C) = 4 + 5 - 1 = 8

Answer 2

n(B∪C) = 6

Explanation:

Given the following sets:

B = {d, p, q, z}

C = {v, w, x, y, z}

We can use the Addition Principle for Counting:

n(B∪C) = n(B) + n (C) - n(B∩C):

where:

n(B) is the number of elements in set B,

n(C) = number of elements in set C,

n(B∩C) = the intersection of sets B and C.

Cardinal number or cardinality is defined as the number of elements in a set.

Looking into the given sets, the similar elements between sets B and C is z, (cardinality = 1). This similar element represents the n(B∩C).

The cardinal number of set B represented by n(B), is the number of distinct elements in set B. Therefore, the cardinality of n(B) = 3

And the cardinality of set c, n(C) = 4

Plugging in these values into the Addition Counting Principle:

n(B∪C) = n(B) + n (C) - n(B∩C)

n(B∪C) = 3 + 4 - 1

n(B∪C) = 6

Attached is the Venn diagram that represents the elments in sets B and C, and the n(B∩C) = z = 1.