Advertisements
Advertisements
प्रश्न
Prove that the following pair of statement pattern is equivalent.
~(p ∧ q) and ~p ∨ ~q
Advertisements
उत्तर
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| p | q | ~p | ~q | p∧q | ~(p∧q) | ~p∨~q |
| T | T | F | F | T | F | F |
| T | F | F | T | F | T | T |
| F | T | T | F | F | T | T |
| F | F | T | T | F | T | T |
In the above table, entries in columns 6 and 7 are identical.
∴ Statement ~(p ∧ q) and ~p ∨ ~q are equivalent.
APPEARS IN
संबंधित प्रश्न
Using truth table, examine whether the following statement pattern is tautology, contradiction or contingency: p ∨ [∼(p ∧ q)]
Express the following statement in symbolic form and write its truth value.
"If 4 is an odd number, then 6 is divisible by 3."
Show that the following statement pattern in contingency :
(~p v q) → [p ∧ (q v ~ q)]
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)
Using the truth table prove the following logical equivalence.
(p ∨ q) → r ≡ (p → r) ∧ (q → r)
Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
(p → q) ↔ (∼ p ∨ q)
Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
[p → (∼ q ∨ r)] ↔ ∼ [p → (q → r)]
(p ∧ q) → r is logically equivalent to ________.
Determine whether the following statement pattern is a tautology, contradiction, or contingency:
[(p ∨ q) ∧ ∼p] ∧ ∼q
Prepare truth tables for the following statement pattern.
(p ∧ r) → (p ∨ ~ q)
Examine whether the following statement pattern is a tautology, a contradiction or a contingency.
q ∨ [~ (p ∧ q)]
Show that the following statement pattern is contingency.
p ∧ [(p → ~ q) → q]
Write the dual of the following:
(p ∨ q) ∨ r
Write the dual statement of the following compound statement.
Radha and Sushmita cannot read Urdu.
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.
Some continuous functions are differentiable.
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) ∧ (q ∧ r)] ∨ (~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)] ∧ r ≡ r
Using the truth table, prove the following logical equivalence.
p ∧ (~p ∨ q) ≡ p ∧ q
Write the converse, inverse, contrapositive of the following statement.
If a man is bachelor, then he is happy.
Choose the correct alternative:
If p → q is an implication, then the implication ~q → ~p is called its
Which of the following is not true for any two statements p and q?
Examine whether the following statement pattern is a tautology or a contradiction or a contingency:
(∼p ∧ ∼q) → (p → q)
Prepare truth table for the statement pattern `(p -> q) ∨ (q -> p)` and show that it is a tautology.
