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WAEC Mathematics 2014 Paper

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Question : 8

Total: 49

If x = {0, 2, 4, 6}, y = {1, 2, 3, 4} and z = {1, 3} are subsets of u = {x:0

\geq

\geq

\cap

\cup

Z)

{0, 2, 6}
{1, 3}
{0, 6)
{9}

Solution:

Concept:

To find

x \cap (Y' \cup Z)

, first determine the complement of set

Y

within the universal set

u

, then perform union and intersection operations.

Explanation:

Given universal set

u = \{x : 0 \le x \le 6\} = \{0, 1, 2, 3, 4, 5, 6\}

.

The sets are

x = \{0, 2, 4, 6\}

,

y = \{1, 2, 3, 4\}

, and

z = \{1, 3\}

.

The complement of

y

is

y' = u - y = \{0, 5, 6\}

.

First, compute

y' \cup z = \{0, 5, 6\} \cup \{1, 3\} = \{0, 1, 3, 5, 6\}

.

Now, intersect this with

x

:

x \cap (y' \cup z) = \{0, 2, 4, 6\} \cap \{0, 1, 3, 5, 6\} = \{0, 6\}

.

Thus, the required set is

\{0, 6\}

.

Answer:

\{0, 6\}

(Option C).

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