JAMIA 2023 — Mathematics PYQ

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Question

JAMIA 2023 — Mathematics PYQ

JAMIA | Mathematics | 2023

How many elements does the set P({𝜑,a,{𝑎},{ {𝑎}}})has; where a & b are distinct elements, P denotes power set.

Choose the correct answer:

Explanation

Given the set:

S = \{\phi, a, \{a\}, \{\{a\}\}\}

Where:

$\phi$ (the empty set) is the first element.
$a$ is the second element.
$\{a\}$ (the set containing $a$ ) is the third element.
$\{\{a\}\}$ (the set containing the set $\{a\}$ ) is the fourth element.

Note: Although the problem mentions " $a$ and $b$ are distinct elements," the element $b$ does not appear in the set $S$ , so it does not affect the count.

The number of elements in set $S$ , denoted as $n(S)$ , is:

n(S) = 4

The number of elements in the power set $P(S)$ is given by the formula:

|P(S)| = 2^{n(S)}

Substituting the value of $n(S)$ :

|P(S)| = 2^4

|P(S)| = 16

Final Answer: The set $P(\{\phi, a, \{a\}, \{\{a\}\}\})$ has 16 elements.