Given the universal set \mathcal{E} = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}, set A = \{1, 2, 4… — JAMB UTME

Given the universal set $\mathcal{E} = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$ , set $A = \{1, 2, 4, 5, 8\}$ , and set $B = \{2, 3, 5, 7, 9\}$ , what is $(A \cup B)'$ ?

$\{6, 10\}$ Answer
B
$\{1, 4, 8\}$
C
$\{3, 6, 7, 9, 10\}$
D
$\{2, 5\}$

Answer

The set

\{6, 10\}

Combining set

A

and set

B

gives

A \cup B = \{1, 2, 3, 4, 5, 7, 8, 9\}

. The complement

(A \cup B)'

contains the elements of the universal set

\mathcal{E}

that are not in this union, which are

6

and

10

, giving

\{6, 10\}

Step-by-Step Solution

Find the union of set

A

and set

B

(

A \cup B

)

A \cup B = \{1, 2, 3, 4, 5, 7, 8, 9\}

The union combines all distinct elements present in set

A

, set

B

, or both.

Determine the complement of

(A \cup B)

with respect to the universal set

\mathcal{E}

(A \cup B)' = \mathcal{E} \setminus (A \cup B) = \{6, 10\}

The complement consists of all elements in the universal set

\mathcal{E}

that are not present in

A \cup B

Key Concept

Set Union and Set Complement

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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