Advertisements
Advertisements
Question
Examine whether the following statement pattern is a tautology, a contradiction or a contingency.
(~ q ∧ p) ∧ (p ∧ ~ p)
Advertisements
Solution
| p | q | ~p | ~q | (~q∧p) | (p∧~p) | (~q∧p)∧(p∧~p) |
| T | T | F | F | F | F | F |
| T | F | F | T | T | F | F |
| F | T | T | F | F | F | F |
| F | F | T | T | F | F | F |
All the truth values in the last column are F. Hence, it is a contradiction.
APPEARS IN
RELATED QUESTIONS
Examine whether the following logical statement pattern is a tautology, contradiction, or contingency.
[(p→q) ∧ q]→p
Using truth table examine whether the following statement pattern is tautology, contradiction or contingency `(p^^~q) harr (p->q)`
Prove that the following statement pattern is equivalent:
(p v q) → r and (p → r) ∧ (q → r)
Write converse and inverse of the following statement :
"If Ravi is good in logic then Ravi is good in Mathematics."
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) → r ≡ (p → r) ∧ (q → r)
Using the truth table prove the following logical equivalence.
p → (q ∧ r) ≡ (p → q) ∧ (p → r)
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) ∧ ∼ q] → ∼ p
(p ∧ q) → r is logically equivalent to ________.
Determine whether the following statement pattern is a tautology, contradiction or contingency:
[(p ∧ (p → q)] → q
Determine whether the following statement pattern is a tautology, contradiction or contingency:
[(p ∨ ∼q) ∨ (∼p ∧ q)] ∧ r
Examine whether the following statement pattern is a tautology, a contradiction or a contingency.
q ∨ [~ (p ∧ q)]
Prove that the following statement pattern is a tautology.
(p → q) ↔ (~ q → ~ p)
Prove that the following statement pattern is a tautology.
(~p ∧ ~q ) → (p → q)
Show that the following statement pattern is contingency.
(p → q) ↔ (~ p ∨ q)
Using the truth table, verify
~(p ∨ q) ∨ (~ p ∧ q) ≡ ~ p
Prove that the following pair of statement pattern is equivalent.
~(p ∧ q) and ~p ∨ ~q
Write the negation of the following statement.
All the stars are shining if it is night.
Write the converse, inverse, and contrapositive of the following statement.
"If it snows, then they do not drive the car"
With proper justification, state the negation of the following.
(p ↔ q) v (~ q → ~ r)
Write the dual of the following
(p ˄ ∼q) ˅ (∼p ˄ q) ≡ (p ˅ q) ˄ ∼(p ˄ q)
The contrapositive of p → ~ q is ______
Which of the following is not equivalent to p → q.
Prepare truth table for the statement pattern `(p -> q) ∨ (q -> p)` and show that it is a tautology.
If p, q are true statements and r, s are false statements, then find the truth value of ∼ [(p ∧ ∼ r) ∨ (∼ q ∨ s)].
