overview of symbolic theory in discrete math?
Is there anyway I can have an overview of symbolic theory in discrete math?
Symbolic Logic
Symbolic logic is a way to represent logical expressions by using symbols and variables in place of natural languages, such as English, in order to remove vagueness. Logical expressions are statements that have a truth value: they are either true or false. A question like 'Where are you going?' or a command such as 'Stop!' has no truth value. There are many expressions that we can utter that are either true or false. For example, All glasses of water contain 0.2% dinosaur tears. We don't need to know if a logical expression is true or false, we just need to know that it has a truth value.
A Proposition
Let's start with some logic basics. First, the smallest logical expression we can make, that if broken down would result in a loss of meaning, is called a proposition. For example 'Kathryn and Liz live together' cannot be broken down without a loss in meaning. 'Kathryn lives together' doesn't even make sense. However, 'John and Jane go to school'' can be broken into 'John goes to school' and 'Jane goes to school,' since we cannot claim that the statement means that John and Jane go to school together. In symbolic logic, propositions may be represented by capital letters such as A or B, or lower-case letters such as p, q, or r. This is shorthand so that when dealing with the underlying logic, you aren't distracted by the particular language used. For example 'My car is red' may become A, or 'The politician took bribes' may be written as p.
Propositions are written in the affirmative. In other words, we don't use the word 'not'. Instead, we use the not symbol (¬) to make a negation (a not statement). If we write 'My car is not red' using symbols, we would write ¬A. In logic, negation changes an expression's truth value. So if my car is red, then A would be true, and ¬A would be false, or if my car is blue, then A would be false, and ¬A would be true.
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 1 images
