# Monthly Archives: October 2023

## Day 59 – 1.205 Laws of sets: Commutative, associative and distributives – Set Identities

Set Identities: 1 – Commutativity Changing the order of elements won’t affect the results. Example in Arithmetics: 5 + 4 = 4 + 5 = 9 and 3 x 1 = 1 x 3 = 3 The addition and multiplication … Continue reading

## Day 58 – Logic Laws

We can use logical equivalences to reduce complex formulas into simpler ones. Two new symbols Identity Law P and True will be true when both P and Tautology are true. P or False will be true when either is true, … Continue reading

## Day 57 – Proofs with Truth Tables

Proofs using Truth Tables Formulas p and q are logically equivalent iff the truth conditions of p are the same as the truth conditions of q. p q x x y y Examples: p q p∧q p∨q ¬(p∨q) 1 1 … Continue reading

## Day 56 – Truth Tables

Review: Each statement is TRUE (1) or FALSE (0). All connectives take a truth value and output a truth value.It means that depending on the connective, the truth value can change. Negation The negation is always the opposite of the … Continue reading

## Day 55 – Propositional Logic

Propositional Logic A statement is a declarative sentence that can be True (1) or False (0). Examples: We cannot express things like questions, as questions cannot be true or false. We also cannot express with imperatives or commands, as those … Continue reading

## Day 54 – De Morgan’s Law

De Morgan’s laws describe how mathematical statements and concepts are related through their opposites. In set theory, De Morgan’s laws relate to the intersection and union of sets through their complements. The structure of De Morgan’s laws, whether applied to … Continue reading

## Day 53 – Set Representation and Manipulation

Universal Set A universal set is a set that contains everything. We note the universal set with the letter U. Venn Diagrams A Venn diagram is used to visualize the possible relations among a collection of sets. U is called … Continue reading

## Day 52 – Alphabets and Strings in Discrete Math

A string is a finite sequence of symbols from an alphabet. A set of binary. The notation above means strings of combinations of 0 and 1. Example: A set of English alphabet. Strings: No limit, sets of strings from the … Continue reading

## Day 51 – Algebra Review Part 1

Combining Like Terms Combining like terms with negative coefficients & distribution We group same terms. We use the precedent when noting negative or positive. Combining like terms with negative coefficients Note y is different y2. They cannot be added nor … Continue reading