Advertisements
Advertisements
Question
Using the truth table, prove the following logical equivalence.
p ∧ (~p ∨ q) ≡ p ∧ q
Advertisements
Solution
| 1 | 2 | 3 | 4 | 5 | 6 |
| p | q | ~p | ~p∨q | p∧(~p∨q) | p∧q |
| T | T | F | T | T | T |
| T | F | F | F | F | F |
| F | T | T | T | F | F |
| F | F | T | T | F | F |
In the above truth table, the entries in columns 5 and 6 are identical.
∴ p ∧ (~p ∨ q) ≡ p ∧ q
APPEARS IN
RELATED QUESTIONS
Using truth table examine whether the following statement pattern is tautology, contradiction or contingency `(p^^~q) harr (p->q)`
Prove that the following statement pattern is a tautology : ( q → p ) v ( p → q )
Using truth table, examine whether the following statement pattern is tautology, contradiction or contingency: p ∨ [∼(p ∧ q)]
Write the negation of the Following Statement :
∀ y ∈ N, y2 + 3 ≤ 7
Write the negation of the following statement :
If the lines are parallel then their slopes are equal.
Using the truth table prove the following logical equivalence.
p ↔ q ≡ ∼ [(p ∨ q) ∧ ∼ (p ∧ q)]
Using the truth table, prove the following logical equivalence.
p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)
Using the truth table proves the following logical equivalence.
∼ (p ↔ q) ≡ (p ∧ ∼ q) ∨ (q ∧ ∼ p)
Inverse of statement pattern (p ∨ q) → (p ∧ q) is ________ .
Determine whether the following statement pattern is a tautology, contradiction or contingency:
[p → (q → r)] ↔ [(p ∧ q) → r]
Examine whether the following statement pattern is a tautology, a contradiction or a contingency.
q ∨ [~ (p ∧ q)]
Prove that the following statement pattern is a tautology.
(~ p ∨ ~ q) ↔ ~ (p ∧ q)
Show that the following statement pattern is contingency.
(p∧~q) → (~p∧~q)
Using the truth table, verify
~(p → ~q) ≡ p ∧ ~ (~ q) ≡ p ∧ q.
Prove that the following pair of statement pattern is equivalent.
p ↔ q and (p → q) ∧ (q → p)
Write the dual of the following:
~(p ∨ q) ∧ [p ∨ ~ (q ∧ ~ r)]
Write the dual statement of the following compound statement.
A number is a real number and the square of the number is non-negative.
Write the negation of the following statement.
All the stars are shining if it is night.
With proper justification, state the negation of the following.
(p → q) ∨ (p → r)
Determine whether the following statement pattern is a tautology, contradiction, or contingency.
[~(p ∧ q) → p] ↔ [(~p) ∧ (~q)]
Determine whether the following statement pattern is a tautology, contradiction, or contingency.
[p → (~q ∨ r)] ↔ ~[p → (q → r)]
Using the truth table, prove the following logical equivalence.
[~(p ∨ q) ∨ (p ∨ q)] ∧ r ≡ r
Write the converse, inverse, contrapositive of the following statement.
If 2 + 5 = 10, then 4 + 10 = 20.
Write the converse, inverse, contrapositive of the following statement.
If a man is bachelor, then he is happy.
Write the dual of the following.
~(p ∨ q) ≡ ~p ∧ ~q
If p → (∼p v q) is false, then the truth values of p and q are respectively
The equivalent form of the statement ~(p → ~ q) is ______.
Which of the following is not true for any two statements p and q?
Using truth table verify that:
(p ∧ q)∨ ∼ q ≡ p∨ ∼ q
Prepare truth table for the statement pattern `(p -> q) ∨ (q -> p)` and show that it is a tautology.
