Linear Algebra Chapter 1.4 - 1.9 Flashcards
What are 12 logic notations and what do they mean?
Check #1 on pg.15
What is #1 definition? Hint: subsets
Check #1 definition on page 15
Define propositional logic
It is a branch of mathematics that studies the value of logic statements
What are the main building blocks of any theorem?
Statements or propositions
What are five statement with p and q?
Check #2 on page 16
What are the three theorems and how do we prove them?
- “if, then” theorem is a theorem of the form “If p, then q”. The proposition p is called premise or hypothesis and q is referred to as conclusion or thesis. We will prove this type of theorem using direct proof, proof by contraposition or proof by contradiction.
- “If and only if” theorem is a theorem of the form “p if and only if q”. It states that p and q are equivalent propositions and can be proved by splitting it into two “if, then” theorems.
- Equivalent statements is a generalization of the “if and only if” theorem is a theorem of the form “The following statements are equivalent: p, q, and r”. We can show this theorem by proving that “p->q”, “q->r” and “r->p” hold true.
What are five proof strategies and what are they about?
Check page 17-19
Prove theorem 1
Check theorem 1 on page 17
Prove number theory
Check number theory (theorem 2) on page.18
Prove theorem 3
Check theorem 3 on page. 18
Prove theorem 4.
Check theorem 4 on pg. 19
Prove the statement is false on page.19
Check counter examples on page 19- 20
What is 5# definition? Hint: expression and linear combination
Check 5#definition on pg.12
What is 6# properties and proof of the first properties? 2 things
Check 6# properties on backside of pg.13
What is 7# theorem and prove it
Check 7# theorem and proof on pg.14
