Given the universal set U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} and a subset P = \{x \in U :… — JAMB UTME

Given the universal set $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$ and a subset $P = \{x \in U : x \text{ is a prime number}\}$ , which of the following sets represents the complement of $P$ , denoted as $P'$ ?

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

Answer

The set

\{1, 4, 6, 8, 9, 10\}

The prime numbers in

U

are

2, 3, 5,

and

7

, making

P = \{2, 3, 5, 7\}

. The complement

P'

consists of all elements in

U

that do not belong to

P

, which yields

\{1, 4, 6, 8, 9, 10\}

Step-by-Step Solution

Identify the elements of the universal set

U

U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}

The universal set defines the boundary of all possible elements under consideration.

Identify the elements belonging to set

P

(prime numbers in

U

)

P = \{2, 3, 5, 7\}

Prime numbers have exactly two distinct positive divisors: 1 and themselves. Note that 1 is not a prime number.

Compute the complement

P' = U \setminus P

P' = \{1, 4, 6, 8, 9, 10\}

The complement of set

P

consists of all elements present in

U

that are not present in

P

Key Concept

Set Complement and Universal Set Boundaries

Estimated Time:45s

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