Exercise 0.1.2(Stability for addition)

Question

Prove that if $P, Q \in \mathcal B$, then $P + Q \in \mathcal B$.

Abdullah Zubair · Accepted Answer

Let $P, Q \in \mathcal B$. Then
\begin{align*}
	(P + Q)M &= PM + QM 	ag{Left dist}\
	&= MP + MQ 	ag{Hypothesis}\
	&= M(P + Q) 	ag{Right dist}
.\end{align*}

Exercise 0.1.2(Stability for addition)

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Exercise 0.1.2(Stability for addition)

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