Tautologies

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

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POINTS (1)

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A tautology is _ by its very structure

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intrinsically true

intrinsically false

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POINTS (1)

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

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True

False

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POINTS (1)

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The following statement is a tautology

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A ∨ A'

True

False

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POINTS (1)

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

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POINTS (1)

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A contradiction is _ __ by its very structure

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intrinsically true

intrinsically false

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POINTS (1)

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Mark the following statements as tautology or contradiction

(1) A ∨ A'
(2) A ∧ A'
(3) (A → B) ↔ (B′ → A′)
(4) (A ∨ A′) → (B ∨ B′)

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tautology

contradiction

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POINTS (1)

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

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True

False

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POINTS (1)

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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. In this case P and Q are said to be equivalent wffs, denoted by

P ⇄ Q

P ⇌ Q

P ⇔ Q

P ⇿ Q

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POINTS (1)

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Explanation

Is the following an equivalent wffs?

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(A → B) ⇔ (B' → A')

Yes

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POINTS (1)

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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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POINTS (1)

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

Correct Answer

Explanation

A tautology is ______ _______ by its very structure

Correct Answer

Explanation

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

Correct Answer

Explanation

The following statement is a tautology

Correct Answer

Explanation

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

Correct Answer

Explanation

A contradiction is _____ ______ by its very structure

Correct Answer

Explanation

Mark the following statements as tautology or contradiction

Correct Answer

Explanation

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

Correct Answer

Explanation

Equivalent wffs

Correct Answer

Explanation

Is the following an equivalent wffs?

Correct Answer

Explanation

Some Tautological Equivalences

Correct Answer

Explanation

Quran Recitation

A tautology is _ by its very structure

A contradiction is _ __ by its very structure