Advertisements
Advertisements
प्रश्न
Using the truth table, verify
~(p ∨ q) ∨ (~ p ∧ q) ≡ ~ p
उत्तर
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| p | q | ~p | (p∨q) | ~(p∨q) | ~p∧q | ~(p∨q)∨(~p∧q) |
| T | T | F | T | F | F | F |
| T | F | F | T | F | F | F |
| F | T | T | T | F | T | T |
| F | F | T | F | T | F | T |
In the above truth table, the entries in columns 3 and 7 are identical.
∴ ~(p ∨ q) ∨ (~ p ∧ q) ≡ ~ p
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 "
Using truth table examine whether the following statement pattern is tautology, contradiction or contingency `(p^^~q) harr (p->q)`
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
By constructing the truth table, determine whether the following statement pattern ls a tautology , contradiction or . contingency. (p → q) ∧ (p ∧ ~ q ).
Examine whether the following statement (p ∧ q) ∨ (∼p ∨ ∼q) is a tautology or contradiction or neither of them.
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.
∼ (∼ q ∧ p) ∧ q
Determine whether the following statement pattern is a tautology, contradiction or contingency:
[(p ∨ ∼q) ∨ (∼p ∧ q)] ∧ r
Determine whether the following statement pattern is a tautology, contradiction or contingency:
(p → q) ∨ (q → p)
Prepare truth tables for the following statement pattern.
p → (~ p ∨ q)
Prove that the following statement pattern is a tautology.
(p → q) ↔ (~ q → ~ p)
Prove that the following statement pattern is a contradiction.
(p ∧ q) ∧ ~p
Prove that the following statement pattern is a contradiction.
(p ∧ q) ∧ (~p ∨ ~q)
Using the truth table, verify.
p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)
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 converse, inverse, and contrapositive of the following statement.
"If it snows, then they do not drive the car"
Construct the truth table for the following statement pattern.
(p ∧ ~ q) ↔ (q → p)
Construct the truth table for the following statement pattern.
(p ∧ r) → (p ∨ ~q)
Construct the truth table for the following statement pattern.
(p ∨ ~q) → (r ∧ p)
What is tautology? What is contradiction?
Show that the negation of a tautology is a contradiction and the negation of a contradiction is a tautology.
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) → p] ↔ [(~p) ∧ (~q)]
Determine whether the following statement pattern is a tautology, contradiction, or contingency.
[p → (~q ∨ r)] ↔ ~[p → (q → r)]
Write the dual of the following.
p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (q ∨ r)
Write the converse and contrapositive of the following statements.
“If a function is differentiable then it is continuous”
Write the dual of the following
(p ˄ ∼q) ˅ (∼p ˄ q) ≡ (p ˅ q) ˄ ∼(p ˄ q)
Choose the correct alternative:
If p → q is an implication, then the implication ~q → ~p is called its
Examine whether the statement pattern
[p → (~ q ˅ r)] ↔ ~[p → (q → r)] is a tautology, contradiction or contingency.
Using truth table verify that:
(p ∧ q)∨ ∼ q ≡ p∨ ∼ q
Show that the following statement pattern is a contingency:
(p→q)∧(p→r)
The converse of contrapositive of ∼p → q is ______.
Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
(p ∧ q) → (q ∨ p)
In the triangle PQR, `bar(PQ) = 2bara and bar(QR)` = `2 bar(b)` . The mid-point of PR is M. Find following vectors in terms of `bar(a) and bar(b)` .
- `bar(PR)`
- `bar(PM)`
- `bar(QM)`
