Let $P = \{a, b, c\}$, $Q = \{a, b, c, d, e\}$ and $R = \{a, b, c\}$. State, giving reasons, which of the following are true: (i) $P \subseteq Q$ (ii) $P \subset Q$ (iii) $P \subseteq R$ (iv) $P \subset R$ (v) $Q \supset P$.

Let P = \a, b, c\, Q = \a, b, c, d, e\ and R = \a, b, c\. State, giving reasons, which of the following are tr

Exercises · Q9

P = \{a, b, c\}

(i)

P \subseteq Q

(ii)

P \subset Q

(iii)

P \subseteq R

(iv)

P \subset R

(v)

Q \supset P

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(i) $P \subseteq Q$ : every element of $P$ ( $a, b, c$ ) is in $Q$ . True.

(ii) $P \subset Q$ : $P \subseteq Q$ holds (from (i)), and $Q$ has extra elements $d, e$ that $P$ lacks, so $P \ne Q$ . True.

(iii) $P \subseteq R$ : every element of $P$ is in $R$ (in fact $P$ and $R$ list exactly the same elements, $a, b, c$ ). True. …