Problem 19

Explanation

Drawing a conclusion using Disjunctive Syllogism.

Let:

• $p$ = Community service to clean gutters is carried out.
• $q$ = Community service to collect used goods is carried out.

Premise 1: On Sunday, community service will be held to clean the gutters or collect used goods ($p \lor q$).

Premise 2: On Sunday, it rained, so the community service to clean the gutters could not be carried out ($\sim p$).

The conclusion from these two premises is:

Meaning: On Sunday, community service to collect used goods was carried out.