# Tautologies

👁 87
statistics

Always true formula

Questions #: 11
Time: 5 minutes
Pass Score: 80.0%
Style
Mode

Missing
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A ∨ A'

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Missing
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#### Mark the following statements as tautology or contradiction

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
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#### Equivalent wffs

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?

(A → B) ⇔ (B' → A')

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#### Some Tautological Equivalences

Assign the right properties to the rows

 A ∨ B ⇔ B ∨ A A ∧ B ⇔ B ∧ A (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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