Tag Archives: CM1020

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 50 – Solving Quadratics by Factoring

We’re asked to solve for s. This is a quadratic equation. The best way to solve this as it’s equal to 0 is to factor the left-hand side, and then think about the fact that those binomials that you factor … Continue reading

Day 49 – The Language of Sets

The foundation of set theory was laid by the eminent German Mathematician Georg Cantor during the latter part of the 19th century. The following are some of the problems we shall pursue in this chapter: Set is a collection of … Continue reading