Question

Find the symmetric difference between the set P and Q.
$P=\{2,3,5,7,11\}$ and $Q=\{1,3,5,11\}$

• A. $\{2,7\}$
• B. $\{1,2,7\}$
• C. $\{3,5,11\}$
• D. $\{1,3,5,11\}$

Answer 1

The correct option is B $\{1,2,7\}$

Given,
$P=\{2,3,5,7,11\}$
$Q=\{1,3,5,11\}$

Now,
$P–Q=\{2,3,5,7,11\}–\{1,3,5,11\}=\{2,7\}$
$Q–P=\{1,3,5,11\}–\{2,3,5,7,11\}=\left\{1\right\}$

$P\Delta Q=(P–Q)\cup (Q–P)$
$=\{2,7\}\cup \left\{1\right\}$
$=\{1,2,7\}$