WEEK 3 JOURNAL: CONJUNCTION, DISJUNCTION, NEGATION AND IMPLICATION

    This week, we learned the elements of language of math. In math, we use "and" to represent conjunction relationship. The "and" in math  is different from the "and" in English. For example, in math, if I say A and B, I mean both A and B are correct. But in English, if I say x = 1 and x = 2, what I really want to say is that x is either 1 or 2. In math, if we want to say x is either 1 or 2, we need to use "or". "Or" means disjunction. In math, A or B means that there is at least one correct statement between A and B. We use "∧"  to represent conjunction and "∨" to represent disjunction.

    Then we learned how to write a negation of a statement. We can translate the statement from math language to English, and negate the statement in English, and translate our negation into math language. 

    Finally we learned how to construct a truth table. In the truth table, we have our inputs and outputs.

the inputs are some statements and whether they are T or F, and the outputs enumerates over all possible combinations of input values. The truth table can help us evaluate expressions (whether it is true of false) in a quicker way. 

    After learning this week's stuff, I find that expressing statements in math language is precise and efficient.