Advertisements
Advertisements
Question
Using the truth table, prove the following logical equivalence.
p ∧ (~p ∨ q) ≡ p ∧ q
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)`
Write the dual of the following statements:
Madhuri has curly hair and brown eyes.
Write converse and inverse of the following statement:
“If a man is a bachelor then he is unhappy.”
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)]
Use the quantifiers to convert the following open sentence defined on N into true statement
5x - 3 < 10
Use the quantifiers to convert the following open sentence defined on N into true statement:
x2 ≥ 1
Prove that the following statement pattern is equivalent:
(p v q) → r and (p → r) ∧ (q → r)
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.
State if the following sentence is a statement. In case of a statement, write down the truth value :
Every quadratic equation has only real roots.
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)
Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
(p ∧ q) → (q ∨ p)
(p ∧ q) → r is logically equivalent to ________.
Determine whether the following statement pattern is a tautology, contradiction or contingency:
[p → (q → r)] ↔ [(p ∧ q) → r]
Determine whether the following statement pattern is a tautology, contradiction or contingency:
(p ∧ q) ∨ (∼p ∧ q) ∨ (p ∨ ∼q) ∨ (∼p ∧ ∼q)
Examine whether the following statement pattern is a tautology, a contradiction or a contingency.
(~ q ∧ p) ∧ (p ∧ ~ p)
Show that the following statement pattern is contingency.
(p∧~q) → (~p∧~q)
Using the truth table, verify.
p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)
Using the truth table, verify
p → (p → q) ≡ ~ q → (p → q)
Prove that the following pair of statement pattern is equivalent.
p ↔ q and (p → q) ∧ (q → p)
Prove that the following pair of statement pattern is equivalent.
p → q and ~ q → ~ p and ~ p ∨ q
Write the dual of the following:
~(p ∨ q) ∧ [p ∨ ~ (q ∧ ~ r)]
Write the dual statement of the following compound statement.
Karina is very good or everybody likes her.
Write the dual statement of the following compound statement.
A number is a real number and the square of the number is non-negative.
Construct the truth table for the following statement pattern.
(p ∧ r) → (p ∨ ~q)
Determine whether the following statement pattern is a tautology, contradiction, or contingency.
[~(p ∧ q) → p] ↔ [(~p) ∧ (~q)]
Using the truth table, prove the following logical equivalence.
p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)
Using the truth table, prove the following logical equivalence.
~p ∧ q ≡ [(p ∨ q)] ∧ ~p
Write the dual of the following.
(~p ∧ q) ∨ (p ∧ ~q) ∨ (~p ∧ ~q)
Write the dual of the following.
(p ∧ q) ∧ r ≡ p ∧ (q ∧ r)
Write the dual of the following.
p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (q ∨ r)
The false statement in the following is ______.
Choose the correct alternative:
If p is any statement, then (p ˅ ~p) is a
Examine whether the statement pattern
[p → (~ q ˅ r)] ↔ ~[p → (q → r)] is a tautology, contradiction or contingency.
Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
(p ∧ q) → (q ∨ p)
