Tautologies

Always true formula

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QUESTION OF
Views #: 813
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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volume_mute
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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 β†’ B) ↔ (Bβ€² β†’ Aβ€²)Β 
  4. (4) (A ∨ Aβ€²) β†’ (B ∨ Bβ€²)Β 
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tautology
contradiction
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β€œToday is Tuesday and today is not Tuesday” is a contradiction

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volume_mute
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Equivalent wffs

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

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Is the following an equivalent wffs?

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(A β†’ B) ⇔ (B' β†’ A')

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Some Tautological Equivalences

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Assign the right properties to the rows

A ∨ B ⇔ B ∨ AΒ  A ∧ B ⇔ B ∧ AΒ  (1)
(A ∨ B) ∨ C ⇔ A ∨ (B ∨ C) (A ∧ B) ∧ C ⇔ A ∧ (B ∧ C) (2)
A ∨ (B ∧ C) ⇔ (A ∨ B) ∧ (A ∨ C) A ∧ (B ∨ C) ⇔ (A ∧ B) ∨ (A ∧ C) (3)
A ∨ 0 ⇔ A A ∧ 1 ⇔ A (4)
A ∨ A' ⇔ 1 A ∧ A' ⇔ 0 (5)
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associative
commutative
distributive
complement
identity
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0
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sin-1 cos-1 tan-1 Ο€ e
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( ) 1/x % n!
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4 5 6 – M+
1 2 3 Γ— M-
0 . EXP Γ· MR
Β± RND C = MC
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Year 11