Week 3 Logic

In week 3, we learned logic, which is using symbols to present logical statements. The symbols include conjunction and disjunction etc.

Conjunction, which is "∧", is similar to intersection and is the expression of and in logic. Because conjunction is similar to intersection, conjunction is false if either part is false. For example, for x∈prime number, x = 3 ∧ x = 7 is true, but x = 3 ∧ x = 4 is false.

Disjunction, which is "∨", is similar to union and is the expression of or in logic. In disjuction, it's different from conjunction, disjunction is true if either part is true and is false if both parts are false.

Then, we learned negation, whose symbol is "¬". Negation is the nagated original statement. The original statement is true if its negation is false.

We also learned some standard transformations for negated expressions like  "¬ ∀x ∈ X, .... ⇔ ∃ x ∈ X, ¬....", and then we can use them to negate a statement as well as change the "¬" symbols position in a statement. 

Drawing truth and tabulating truth are two ways to check if an implication is true. We draw Venn diagrams for drawing truth and build tables for all possible outcomes for tabulating truth.