TEZPUR 2025 — Mathematics PYQ

The Cartesian product of two sets $A$ and $B$, denoted as $A\times B$, is the set of all ordered pairs $(x,y)$ such that $x\in A$ and $y\in B$.

Given:

$A=\{1,4\}$

$B=\{a,b\}$

To find $A\times B$, we pair each element of set $A$ with every element of set $B$:

• $1$ paired with $a$: $(1,a)$

• $1$ paired with $b$: $(1,b)$

• $4$ paired with $a$: $(4,a)$

• $4$ paired with $b$: $(4,b)$

Combining these, we get:

$A\times B=\{(1,a),(4,a),(1,b),(4,b)\}$

Comparing this result with the given options, it matches option (a).

Correct Option: (a) $\{(1,a),(4,a),(1,b),(4,b)\}$