Chapter 5: Methods of Proof for Boolean Logic

... for this sentence to be true. That is, we can describe a situation in which a large object adjoins another object. So this sentence is not a logical contradiction. However, there is no Tarski World in which this sentence is true. Hence, it is a TW-contradiction. ...

... for this sentence to be true. That is, we can describe a situation in which a large object adjoins another object. So this sentence is not a logical contradiction. However, there is no Tarski World in which this sentence is true. Hence, it is a TW-contradiction. ...

Quantifiers

... some UD is truth-functionally invalid, then the original argument is FO invalid, but if it is truth-functionally valid, then that does not mean that the original argument is FO valid. • For example, with UD = {a}, the expansion of the argument would be truth-functionally valid. In general, it is alw ...

... some UD is truth-functionally invalid, then the original argument is FO invalid, but if it is truth-functionally valid, then that does not mean that the original argument is FO valid. • For example, with UD = {a}, the expansion of the argument would be truth-functionally valid. In general, it is alw ...

Lecture Notes 3

... If you believe P Q is true you will be asked to select the disjunct that is true. If you believe P Q is false Tarski’s World will attempt to find a disjunct that is true. If you believe P Q is true Tarski’s World will attempt to find a conjunct that is false. If you believe P Q is false you ...

... If you believe P Q is true you will be asked to select the disjunct that is true. If you believe P Q is false Tarski’s World will attempt to find a disjunct that is true. If you believe P Q is true Tarski’s World will attempt to find a conjunct that is false. If you believe P Q is false you ...

Intro to Logic Quiz Game Final

... Suppose for contradiction that x Large(x). Then let ‘a’ name an arbitrary member of the domain. By universal elimination on the assumption and premise 1, we have Large(a) and Large(a) Small(a), so by modus ponens, Small(a). But since a was arbitrary, we can conclude x Small(x). But this contradi ...

... Suppose for contradiction that x Large(x). Then let ‘a’ name an arbitrary member of the domain. By universal elimination on the assumption and premise 1, we have Large(a) and Large(a) Small(a), so by modus ponens, Small(a). But since a was arbitrary, we can conclude x Small(x). But this contradi ...

Section

... the trap of thinking that distinct variables range over distinct objects. In fact, the sentence xyP(x,y) logically implies xP(x,x), and xP(x,x) logically implies xyP(x,y)! ...

... the trap of thinking that distinct variables range over distinct objects. In fact, the sentence xyP(x,y) logically implies xP(x,x), and xP(x,x) logically implies xyP(x,y)! ...

# Rubik's Cube

Rubik's Cube is a 3-D combination puzzle invented in 1974 by Hungarian sculptor and professor of architecture Ernő Rubik.Originally called the Magic Cube, the puzzle was licensed by Rubik to be sold by Ideal Toy Corp. in 1980 via businessman Tibor Laczi and Seven Towns founder Tom Kremer, and won the German Game of the Year special award for Best Puzzle that year. As of January 2009, 350 million cubes had been sold worldwide making it the world's top-selling puzzle game. It is widely considered to be the world's best-selling toy.In a classic Rubik's Cube, each of the six faces is covered by nine stickers, each of one of six solid colours: white, red, blue, orange, green, and yellow. In currently sold models, white is opposite yellow, blue is opposite green, and orange is opposite red, and the red, white and blue are arranged in that order in a clockwise arrangement. On early cubes, the position of the colours varied from cube to cube. An internal pivot mechanism enables each face to turn independently, thus mixing up the colours. For the puzzle to be solved, each face must be returned to have only one colour.Similar puzzles have now been produced with various numbers of sides, dimensions, and stickers, not all of them by Rubik.Although the Rubik's Cube reached its height of mainstream popularity in the 1980s, it is still widely known and used. Many speedcubers continue to practice it and other twisty puzzles and compete for the fastest times in various categories. Since 2003, The World Cube Association, the Rubik's Cube's international governing body, has organised competitions worldwide and kept the official world records.