cse16

    Cards (330)

    • Invertible function

      1. A→B is invertible iff bijective
    • Invertible functions is a function f that has an inverse
    • Sequence
      A function whose domain is a subset of ℕ
    • Geometric sequence
      a type of sequence where each succeeding term is produced by multiplying each preceding term by a fixed number
    • Recurrence relation

      An equation that expresses aₙ in terms of earlier terms: aₙ₋₁, aₙ₋₂, ...
    • Closed formula
      A function of n that satisfies the recurrence relation
    • Summation (or series)
      is the sum of a sequence
    • A way to define a sequence of numbers or values by providing a formula that specifies how the next term is related to previous terms
      A recurrence relation
    • Proposition
      A statement that can be assigned a truth value (True or False)
    • Propositionsexamples
      • It is raining today
      • 2+3=5
      • 2+3=7
    • Negation (not)
      The negation of a proposition P is 'not P'
    • Conjunction 'P and Q'
    • Disjunction (or, inclusive or)
      The disjunction of propositions P and Q is 'P or Q'
    • Exclusive or
      The exclusive or of propositions P and Q is 'P or Q, but not both'
    • Implication (if-then)
      The implication of P to Q is 'if P, then Q'
    • Biconditional (if and only if)
      The biconditional of P and Q is 'P if and only if Q'
    • Atomic Proposition
      A basic proposition that cannot be broken down further
    • Compound Proposition
      A proposition built from atomic propositions and logical operations
    • P → (Q > R) is a meaningful compound proposition, but P → Q → R is meaningless
    • Tautology
      A compound proposition that is true for every assignment of truth values to its propositional variables
    • Contradiction
      A compound proposition that is false for every assignment of truth values to its propositional variables
    • Satisfiable
      A proposition that is not a contradiction
    • Contingency
      A proposition that is neither a tautology nor a contradiction
    • Logically Equivalent
      Two propositions A and B are logically equivalent if A↔B is a tautology
    • P→Q = ¬P∨Q (implication is equivalent to disjunction of negation and consequent)
    • P→Q = ¬Q→¬P (implication is equivalent to the contrapositive)
    • P→Q ≠ ¬P→P (the inverse of an implication is not equivalent)
    • P↔Q = (P→Q)∧(Q→P) (biconditional is equivalent to the conjunction of two implications)
    • P
      9 unless
    • Equivalences
      1.3
    • Tautology
      A compound Prop. that is true for every assignment of truth Values to its Propositional Variables
    • Contradiction
      A compound Prop. that is false for every assignment
    • Tautology
      • P v ~P
    • Contradiction
      • P ^ ~P
    • P -> (P v q) is a tautology
    • Contingency
      A prop. that is neither a tautology nor a contradiction
    • Logically equivalent
      Two Propositions A,B are said to be logically equivalent iff A&B is a tautology
    • Notation: A = B
    • A = B iff A&B have the same truth table
    • Logically equivalent
      • P -> q = ~P v q
      • P => q = ~P v q
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