Tautologies

Always true formula

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QUESTION OF
Views #: 614
Questions #: 11
Time: 5 minutes
Pass Score: 80.0%
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A wff whose truth values are always true, is called a ________

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A tautology is ______ _______ by its very structure

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"Today the sun will shine or today the sun will not shine" is called a Tautology

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The following statement is a tautology

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A ∨ A'

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A wff whose truth values are always false, is called a _______

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A contradiction is _____ ______ by its very structure

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Mark the following statements as tautology or contradiction

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  1. (1) A ∨ A'
  2. (2) A ∧ A'
  3. (3) (A → B) ↔ (B′ → A′) 
  4. (4) (A ∨ A′) → (B ∨ B′) 
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tautology
contradiction
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“Today is Tuesday and today is not Tuesday” is a contradiction

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Equivalent wffs

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Suppose that PQ is a tautology and truth table for all letters in both statements agree for every row.  In this case P and Q are said to be equivalent wffs, denoted by

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Is the following an equivalent wffs?

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(A → B) ⇔ (B' → A')

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Some Tautological Equivalences

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Assign the right properties to the rows

ABBA  ABBA  (1)
(AB) ∨ CA ∨ (BC) (AB) ∧ CA ∧ (BC) (2)
A ∨ (BC) ⇔ (AB) ∧ (AC) A ∧ (B ∨ C) ⇔ (A ∧ B) ∨ (A ∧ C) (3)
A ∨ 0 ⇔ A A ∧ 1 ⇔ A (4)
AA' ⇔ 1 A' ⇔ 0 (5)
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associative
commutative
distributive
complement
identity
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Keywords
Year 11