Question

Consider the following statements
Statement I The Cartesian product of two non-empty sets $P$ and $Q$ is denoted as $P \times Q$ and $P \times Q=\{(p, q): p \in P, q \in Q\}$
Statement II If $A=\{$ red, blue $\}$ and $B=\{b, c, s\}$, then $A \times B=\{($ red,$b),($ red,$c),($ red, $s)$, (blue, $b)$, (blue, $c$ ), (blue, $s)\}$. Choose the correct option.

• A. Statement I is true
• B. Statement II is true
• C. Both are true
• D. Both are false

Answer 1

Answer: (C)

$P$ and $Q$ are two non-empty sets. The Cartesian product $P \times Q$ is the set of all ordered pairs of elements from $P$ and $Q$,
i.e., $P \times Q=\{(p, q): p \in P$ and $q \in Q\}$
Now, $A=\{$ red, blue $\}, B=\{b, c, s\}$
$A \times B=$ Set of all ordered pairs
$=\{($ red,$b),($ red,$c),($ red, $s),($ blue,$b),($ blue,$c),($ blue, $s)\}$