Fourth Week

Sep 9th - Oct 3

• Transitivity
• Order of quantifiers

  Transitivity provide us a tool to make connection between several different statements' relationships.

Just as this statement, If the both sides of Conjunction sigh is true, we can deduce that by drawing a Venn diagram.

  Besides, I learn that the order of quantifiers may cause a big difference to the correctness of a statement.For example, (S1=S2={1,2,3,4})

To the two statements, the up one is true but the bottom one is false. Heap uses a smart instance to reveals the difference of them. If a very worst people want to make a gamble with him, the bad guy say 'if I choose a arbitrary number is S1 could you find a element in S2, that x+y=5.' Heap says 'of course'. Why Heap is so confident because that every time Heap's choice is depending on the bad guys choice. Conversely, if the bad guy wants Heap to choose first, Heap will lose too. The story just want to tell us that the order of the quantifier also carries some logic meanings in it. Hence, we could not use them casually.