Tautologies

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statistics
by Dr. Osama M. Khaled last modified 2022-08-19T00:34:41+00:00

Always true formula

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

A wff whose truth values are always true, is called a ________

Missing
POINTS (1)

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Explanation

A tautology is ______ _______ by its very structure

POINTS (1)

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Explanation

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

POINTS (1)

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Explanation

The following statement is a tautology

A ∨ A'

POINTS (1)

Correct Answer

Explanation

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

Missing
POINTS (1)

Correct Answer

Explanation

A contradiction is _____ ______ by its very structure

POINTS (1)

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Explanation

Mark the following statements as tautology or contradiction

  1. (1) transparent A ∨ A'
  2. (2) transparent A ∧ A'
  3. (3) transparent (A → B) ↔ (B′ → A′) 
  4. (4) transparent (A ∨ A′) → (B ∨ B′) 
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tautology
contradiction
POINTS (1)

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Explanation

“Today is Tuesday and today is not Tuesday” is a contradiction

POINTS (1)

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Explanation

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

POINTS (1)

Correct Answer

Explanation

Is the following an equivalent wffs?

(A → B) ⇔ (B' → A')

POINTS (1)

Correct Answer

Explanation

Some Tautological Equivalences

Assign the right properties to the rows

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

Correct Answer

Explanation

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