The Fundamentals: Natural Language & Symbolic Logic
Fundamentally, CSC165 is about learning how to express yourself through logic and mathematics, which can be accomplished through natural language and symbolic language. Most of us are used to logic in natural language. For example, "If it is bright outside, it must be day time" is a logical statement that guarantees a consequence to it being bright outside. This course would identify this statement as an implication; The first portion is the "antecedent", or something that logically precedes something, which is usually expressed as "P." Furthermore, the latter portion "it being bright outside" is the "consequent", the result which can be expressed as "Q". So therefore, the implication structure is "If P then Q." Symbolically that would look like: P ⇒ Q
Two important concepts we have also learned is universality and existence. The easiest way to explain it is by using a quantified example:
E = {"Dona": 56,000, "Dom": 60, 000, "Sarah": 30, 000, "Joe": 24, 000}
En(x) = x earns more than 25, 000
Given the set of employee's E, we may claim that "Every employee earns more than 25,000." This is a universal statement as it assumes something for "every" (or universally" employee. This would look like:
x 
E, En(x). Universalities can be negated by presenting at least one case in which this statement is false. Which would be the following below: We may suggest then that "There is an employee who makes less than 25, 000." Which would translate to:
x E, EnL(x). That case being Joe. To falsify this would require you to present no examples of this claim.Thoughts on A1
Briefly, A1 hasn't been too difficult. I have basically finished it except for the Venn Diagram section of (4).
