Question

If $P=\{2,4,6,8,10,12\},Q=\{4,6,8\}$ and $R=\{4,6\}$, then which of the following statements is not correct?

• A. $Q\subseteq P$
• B. $P\supseteq R$
• C. $P\supseteq Q$
• D. $Q\subseteq R$

Answer 1

The correct option is D $Q\subseteq R$

Given,
$P=\{2,4,6,8,10,12\},Q=\{4,6,8\}$ and $R=\{4,6\}$

Since, each element of set Q is in set P,
Therefore, $Q\subseteq P$[Q is subset of P].

Since, each element of set Q and Set R in set P.
P is superset of set Q and set R.
Therefore, $P\supseteq R$ and $P\supseteq Q$

Hence, option a, b and c are correct.
'8' is not in set R. Hence, set Q is not subset of R.

Hence, correct option is $Q\subseteq R$.