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, $s)\}$