Question

If $P =\{ a , b , c \}$ and $Q =\{ r \}$, then

• A. $P \times Q = Q \times P$
• B. $P \times Q \neq Q \times P$
• C. $P \times Q \subset Q \times P$
• D. None of these

Answer 1

Answer: (B)

Given $P =\{ a , b , c \}$ and $Q =\{ r \}$
$P \times Q =\{( a , r ),( b , r ),( c , r )\}$
$Q \times P =\{( r , a ),( r , b ),( r , c )\}$
Since, by the definition of equality of ordered pairs,
the pair $( a , r )$ is not equal to the pair $( r , a )$,
we conclude that $P \times Q \neq Q \times P$
However, the number of elements in each set will be the same.