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CS173 Examlet 1 (Self-Study)
UIUC CS173 Proficiency Exam
34
Computer Science
06/03/2018

Term
 set Z
Definition
 integers {..,-1,0,1,....}
Term
 Rewrite[image]
Definition
 [image]
Term
 Rewrite:[image]
Definition
 [image]
Term
 [image]Rewrite
Definition
 [image]
Term
 set N
Definition
 Natural numbersINCLUDES 0{0, 1, 2, 3,...}
Term
 Z+ set
Definition
 positive integers{1, 2, 3, ...}
Term
 set R
Definition
 real numbers - both rational and irrational
Term
 set Q
Definition
 rational numbers (fraction that involves two integers - ex 4/3)
Term
 set C
Definition
 complex numbers
Term
 Floor function
Definition
 ⌊ x ⌋Rounds DOWN functionfloor(-3.75) = -4floor (3.75) = 3
Term
 Ceiling function
Definition
 ⌈ x ⌉Rounds UP functionceiling(-3.75) = -3ceiling(3.75) = 4
Term
 Notation for set membership, and not being in set membership
Definition
 Usex ∈ Z for x is an element of ZCross out ∈ for not an element - similar to not equals to.
Term
 Proposition definition
Definition
 statement that is either true or false (but never both)example: 2 < 15Cannot contain variables (ex: x < 3)
Term
 truth table example for p ∧ q
Definition
 [image]
Term
 ¬p is short for...?
Definition
 "not p"Example: Urbana is not in Illinois
Term
 p ∧ q
Definition
 p and q
Term
 p ∨ q
Definition
 p or q
Term
 p ⊕ q
Definition
 True if only ONE is true.See table:[image]
Term
 p → q truth table
Definition
 p implies q[image]
Term
 Converse of p → q
Definition
 q → p
Term
 p implies q and conversely
Definition
 q ↔ p
Term
 contrapositive
Definition
 negate both p and q, swap their rolesp → q¬q → ¬p
Term
 • If it’s below zero, my car won’t start.Converse and contrapositive this
Definition
 • converse: If my car won’t start, it’s below zero• contrapositive: If my car will start, then it’s not below zero.
Term
 q → p truth table
Definition
 [image]
Term
 q ↔ p truth table
Definition
 [image]
Term
 ¬p ∨ q is equivalent to ____
Definition
 p → q
Term
 Logical Equivalence Symbol
Definition
 ≡Give the same truth table/output
Term
 De Morgan’s Laws
Definition
 ¬(p ∧ q) ≡ ¬p ∨ ¬q¬(p ∨ q) ≡ ¬p ∧ ¬q¬(¬p) ≡ pDistributing in ¬
Term
 p ∨ (q ∧ r) ≡p ∧ (q ∨ r) ≡
Definition
 1. (p ∨ q) ∧ (p ∨ r)2. (p ∧ q) ∨ (p ∧ r)
Term
 ¬(p → q) is
Definition
 p ∧ ¬q
Term
 Negating propositions
Definition
 ¬() around whole statement
Term
 predicate
Definition
 Statement that can be true or false
Term
 Quantifier (English)
Definition
 Expresses a range of values in a domain that make something trueExample in english: “some”,“a couple”, “a few”, “many”, “most.”
Term
 With shorthand and english definitions:universal quantifierexistential quantifierunique existence quantifierHow to combine quantifiers?
Definition
 universal - "for all" - ∀existential - "there exists" - ∃unique existence - "there is a unique" - ∃!Combine with a comma.
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