Advertisements
Advertisements
प्रश्न
Prepare truth tables for the following statement pattern.
p → (~ p ∨ q)
Advertisements
उत्तर
p → (~ p ∨ q)
| p | q | ~p | ~ p ∨ q | p → (~ p ∨ q) |
| T | T | F | T | T |
| T | F | F | F | F |
| F | T | T | T | T |
| F | F | T | T | T |
APPEARS IN
संबंधित प्रश्न
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 "
If p and q are true statements and r and s are false statements, find the truth value of the following :
( p ∧ ∼ r ) ∧ ( ∼ q ∧ s )
Use the quantifiers to convert the following open sentence defined on N into true statement
5x - 3 < 10
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 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.
∼ (∼ q ∧ p) ∧ q
Determine whether the following statement pattern is a tautology, contradiction, or contingency:
[(p ∨ q) ∧ ∼p] ∧ ∼q
Determine whether the following statement pattern is a tautology, contradiction or contingency:
(p → q) ∨ (q → p)
Examine whether the following statement pattern is a tautology, a contradiction or a contingency.
~ p → (p → ~ q)
Using the truth table, verify
~(p ∨ q) ∨ (~ p ∧ q) ≡ ~ p
Write the dual of the following:
(p ∨ q) ∨ r
Write the negation of the following statement.
∀ n ∈ N, n + 1 > 0
Using the rules of negation, write the negation of the following:
~(p ∨ q) → r
With proper justification, state the negation of the following.
(p ↔ q) v (~ q → ~ r)
Construct the truth table for the following statement pattern.
(p ∧ r) → (p ∨ ~q)
Construct the truth table for the following statement pattern.
(p ∨ r) → ~(q ∧ r)
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) ∨ (p ∨ q)] ∧ r ≡ r
Write the converse, inverse, contrapositive of the following statement.
If 2 + 5 = 10, then 4 + 10 = 20.
State the dual of the following statement by applying the principle of duality.
p ∨ (q ∨ r) ≡ ~[(p ∧ q) ∨ (r ∨ s)]
Write the dual of the following.
(p ∧ q) ∧ r ≡ p ∧ (q ∧ r)
The statement pattern (∼ p ∧ q) is logically equivalent to ______.
Write the negation of the following statement:
(p `rightarrow` q) ∨ (p `rightarrow` r)
Show that the following statement pattern is a contingency:
(p→q)∧(p→r)
Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
(p ∧ q) → (q ∨ p)
Prepare truth table for the statement pattern `(p -> q) ∨ (q -> p)` and show that it is a tautology.
