JAMIA 2025 — Mathematics PYQ

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Question

JAMIA 2025 — Mathematics PYQ

JAMIA | Mathematics | 2025

If $A = 1, 2, 3$ and $B = 4, 5$ . what is the number of elements in $A×B$ ?

Choose the correct answer:

Explanation

Solution

1. Given Sets:

Set $A = \{1, 2, 3\}$
Set $B = \{4, 5\}$

2. Finding Cardinality:

The number of elements (cardinality) in each set is:

$n(A) = 3$
$n(B) = 2$

3. Formula for Cartesian Product:

The number of elements in the Cartesian product of two sets $A$ and $B$ is given by the product of the number of elements in each set:

n(A \times B) = n(A) \times n(B)

4. Calculation:

Substituting the values into the formula:

n(A \times B) = 3 \times 2

n(A \times B) = 6

List of Ordered Pairs

To visualize this, we can list all the elements of $A \times B$ :

A \times B = \{(1, 4), (1, 5), (2, 4), (2, 5), (3, 4), (3, 5)\}

Final Answer:

The number of elements in $A \times B$ is 6.