Advertisements
Advertisements
प्रश्न
Prove that the following statement pattern is a contradiction.
(p ∨ q) ∧ (~p ∧ ~q)
Advertisements
उत्तर
| p | q | ~p | ~q | p∨q | ~p∧~q | (p∨q)∧(~p∧~q) |
| T | T | F | F | T | F | F |
| T | F | F | T | T | F | F |
| F | T | T | F | T | F | F |
| F | F | T | T | F | T | F |
All the truth values in the last column are F. Hence, it is a contradiction.
APPEARS IN
संबंधित प्रश्न
Examine whether the following logical statement pattern is a tautology, contradiction, or contingency.
[(p→q) ∧ q]→p
Write the converse and contrapositive of the statement -
“If two triangles are congruent, then their areas are equal.”
Express the following statement in symbolic form and write its truth value.
"If 4 is an odd number, then 6 is divisible by 3 "
Prove that the following statement pattern is equivalent :
(p ∨ q) → r and (p → r) ∧ (q → r)
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.”
Use the quantifiers to convert the following open sentence defined on N into true statement:
x2 ≥ 1
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 :
√-4 is a rational number.
Write converse and inverse of the following statement :
"If Ravi is good in logic then Ravi is good in Mathematics."
Using the truth table prove the following logical equivalence.
∼ (p ∨ q) ∨ (∼ p ∧ q) ≡ ∼ p
Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
(p ∧ q) → (q ∨ p)
Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
[(p → q) ∧ ∼ q] → ∼ p
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)]
Determine whether the following statement pattern is a tautology, contradiction, or contingency:
[(p ∨ q) ∧ ∼p] ∧ ∼q
Prove that the following statement pattern is a contradiction.
(p ∧ q) ∧ ~p
Prove that the following pair of statement pattern is equivalent.
p → q and ~ q → ~ p and ~ p ∨ q
Using the rules of negation, write the negation of the following:
~(p ∨ q) → r
Construct the truth table for the following statement pattern.
(~p ∨ q) ∧ (~p ∧ ~q)
Using the truth table, prove the following logical equivalence.
~p ∧ q ≡ [(p ∨ q)] ∧ ~p
State the dual of the following statement by applying the principle of duality.
2 is even number or 9 is a perfect square.
Write the dual of the following.
(~p ∧ q) ∨ (p ∧ ~q) ∨ (~p ∧ ~q)
Write the dual of the following.
~(p ∨ q) ≡ ~p ∧ ~q
Express the truth of the following statement by the Venn diagram.
Some members of the present Indian cricket are not committed.
Examine whether the statement pattern
[p → (~ q ˅ r)] ↔ ~[p → (q → r)] is a tautology, contradiction or contingency.
Determine whether the following statement pattern is a tautology, contradiction, or contingency:
[(∼ p ∧ q) ∧ (q ∧ r)] ∧ (∼ q)
The statement pattern (∼ p ∧ q) is logically equivalent to ______.
Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
(p ∧ q) → (q ∨ p)
