Tautologies

Always true formula
👁 293
statistics
calculate
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)

Correct Answer

Explanation

A tautology is ______ _______ by its very structure

POINTS (1)

Correct Answer

Explanation

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

POINTS (1)

Correct Answer

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)

Correct Answer

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′) 
drag and drop the selected option to the right place
tautology
contradiction
POINTS (1)

Correct Answer

Explanation

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

POINTS (1)

Correct Answer

Explanation

Equivalent wffs

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

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

A ∨ B ⇔ B ∨ A  A ∧ B ⇔ B ∧ A  (1) transparent
(A ∨ B) ∨ C ⇔ A ∨ (B ∨ C) (A ∧ B) ∧ C ⇔ A ∧ (B ∧ C) (2) transparent
A ∨ (B ∧ C) ⇔ (A ∨ B) ∧ (A ∨ C) A ∧ (B ∨ C) ⇔ (A ∧ B) ∨ (A ∧ C) (3) transparent
A ∨ 0 ⇔ A A ∧ 1 ⇔ A (4) transparent
A ∨ A' ⇔ 1 A ∧ A' ⇔ 0 (5) transparent
drag and drop the selected option to the right place
associative
commutative
distributive
complement
identity
POINTS (1)

Correct Answer

Explanation

Views:
Trials:
Avg score:
0
sin cos tan
sin-1 cos-1 tan-1 π e
xy x3 x2 ex 10x
y√x 3√x √x ln log
( ) 1/x % n!
7 8 9 + MS
4 5 6 – M+
1 2 3 × M-
0 . EXP ÷ MR
± RND C = MC

Document Actions