Week 3: Conjunction, Disjunction, Negation, Implication

The third week of class, the topic we focused on was still the language of math. We learned about different ways to express sets, using conjunctions and disjunctions. Learning this new method means we have more freedom to express what we want to, choosing the appropriate method to do so.

Conjunction is the"action or an instance of two or more events or things occurring at the same point in time or space". To express it in words, it means "and". It means an overlap of events, which is the same as the intersection between 2 or more sets.

Disjunction is combining 2 statements by saying at least one is true. In terms of sets, it can be represented by the union of 2 events.

Our next big topic was negations; negation means "not." We learned the method to negate a statement: the negation sign should apply to the smallest part of the expression. To negate something, we separate it into categories. For a universal quantifier, we negate it with one counter example. For an existential quantification, however, we would need to negate it with a universal quantification. We would need to push the negation sign inside, layer by layer, to make it apply to the smallest part. We also learned about the importance of scope. Everything that happens in scope, stays in scope.

Next, we learned the truth tables. These tables consisted of the possible outputs of all the predicates. However many predicates there are, there are 2^n rows to the table. Truth tables can be used to evaluate expressions involving predicates and implications, as well as for determining satisfiability. Satisfiability can only be satisfied if not all the possible outcomes are the same. Furthermore, truth tables can be used for proving equivalence: if all the outcomes turn out to be the same for every row, we can say these 2 statements are equivalent.