Advertisements
Advertisements
प्रश्न
Examine whether each of the following statement patterns is a tautology or a contradiction or a contingency.
[~(~p ∧ ~q)] v q
उत्तर
Consider the statement pattern: ∼ (∼ p ∧ ∼ q) ∨ q
Thus the truth table of the given logical statement: ~(~p ∧ ~q) ∨ q
| p | q | ~p | ~q | ~p∧~q | ~(~p ∧ ~q) | ~(~p ∧ ~q) ∨ q |
| T | T | F | F | F | T | T |
| T | F | F | T | F | T | T |
| F | T | T | F | F | T | T |
| F | F | T | T | T | F | F |
The above statement is contingency.
APPEARS IN
संबंधित प्रश्न
Using truth table, prove the following logical equivalence:
(p ∧ q) → r ≡ p → (q → r)
Write down the following statements in symbolic form :
(A) A triangle is equilateral if and only if it is equiangular.
(B) Price increases and demand falls
Using truth table prove that ∼p ˄ q ≡ (p ˅ q) ˄ ∼p
Using truth table, prove that ~ p ∧ q ≡ (p ∨ q) ∧ ~ p
Using the truth table, prove the following logical equivalence :
p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)
Evaluate: ∫ x . log x dx
Write converse, inverse contrapositive of the statement "If two triangles are not congruent then their areas are not equal.
Write the following compound statement symbolically.
Angle is neither acute nor obtuse.
Write the following compound statement symbolically.
If Δ ABC is right-angled at B, then m∠A + m∠C = 90°
Write the following compound statement symbolically.
Hima Das wins gold medal if and only if she runs fast.
Write the following compound statement symbolically.
x is not irrational number but is a square of an integer.
Construct the truth table of the following statement pattern.
(p ∧ q) ↔ (q ∨ r)
Construct the truth table of the following statement pattern.
p → [∼ (q ∧ r)]
Construct the truth table of the following statement pattern.
∼ p ∧ [(p ∨ ∼ q) ∧ q]
Construct the truth table of the following statement pattern.
(q → p) ∨ (∼ p ↔ q)
Construct the truth table of the following statement pattern.
[p → (q → r)] ↔ [(p ∧ q) → r]
Construct the truth table of the following statement pattern.
(p ∨ ∼ q) → (r ∧ p)
If p ∧ q is false and p ∨ q is true, then ______ is not true.
Construct the truth table of the following:
p → (q → p)
Construct the truth table of the following:
(∼p ∨ ∼q) ↔ [∼(p ∧ q)]
Construct the truth table of the following:
[(p ∧ q) ∨ r] ∧ [∼r ∨ (p ∧ q)]
Construct the truth table of the following:
[(∼p ∨ q) ∧ (q → r)] → (p → r)
Determine the truth values of p and q in the following case:
(p ∨ q) is T and (p ∨ q) → q is F
Determine the truth values of p and q in the following case:
(p ∧ q) is F and (p ∧ q) → q is T
Express the following statement in symbolic form.
e is a vowel or 2 + 3 = 5
Express the following statement in symbolic form.
Mango is a fruit but potato is a vegetable.
Express the following statement in symbolic form.
Even though it is cloudy, it is still raining.
Write the truth value of the following statement.
Earth is a planet and Moon is a star.
Write the truth value of the following statement.
16 is an even number and 8 is a perfect square.
Write the negation of the following statement.
All men are animals.
Write the negation of the following statement.
− 3 is a natural number.
Write the truth value of the negation of the following statement.
For every x ∈ N, x + 3 < 8.
Write the following statement in symbolic form.
If triangle is equilateral then it is equiangular.
Write the following statement in symbolic form.
It is not true that “i” is a real number.
Write the following statement in symbolic form.
Even though it is not cloudy, it is still raining.
Write the following statement in symbolic form.
Milk is white if and only if the sky is not blue.
Write the following statement in symbolic form.
Stock prices are high if and only if stocks are rising.
Find the truth value of the following statement.
It is not true that 3 − 7i is a real number.
Find the truth value of the following statement.
If a joint venture is a temporary partnership, then discount on purchase is credited to the supplier.
Find the truth value of the following statement.
Neither 27 is a prime number nor divisible by 4.
If p and q are true and r and s are false, find the truth value of the following compound statement.
p ∧ (q ∧ r)
If p and q are true and r and s are false, find the truth value of the following compound statement.
~ [(~ p ∨ s) ∧ (~ q ∧ r)]
If p and q are true and r and s are false, find the truth value of the following compound statement.
(p → q) ↔ ~(p ∨ q)
Assuming that the following statement is true,
p : Sunday is holiday,
q : Ram does not study on holiday,
find the truth values of the following statements.
Sunday is not holiday or Ram studies on holiday.
Assuming that the following statement is true,
p : Sunday is holiday,
q : Ram does not study on holiday,
find the truth values of the following statements.
Sunday is a holiday and Ram studies on holiday.
If p : He swims
q : Water is warm
Give the verbal statement for the following symbolic statement.
~ (p ∨ q)
Fill in the blanks :
Conjunction of two statement p and q is symbolically written as ______.
Fill in the blanks :
Negation of “some men are animal” is –––––––––.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
The Sun has set and Moon has risen.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
Kavita is brilliant and brave.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
If Kiran drives the car, then Sameer will walk.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
The necessary condition for existence of a tangent to the curve of the function is continuity.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
The drug is effective though it has side effects.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
If a real number is not rational, then it must be irrational.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
It is not true that Ram is tall and handsome.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
It is not true that intelligent persons are neither polite nor helpful.
If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.
Proof is lengthy and it is not interesting.
If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.
It is interesting iff the proof is lengthy.
Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.
p → q
Rewrite the following statement without using conditional –
(Hint : p → q ≡ ∼ p ∨ q)
If price increases, then demand falls.
Rewrite the following statement without using conditional –
(Hint : p → q ≡ ∼ p ∨ q)
If demand falls, then price does not increase.
Write the negation of the following.
If ∆ABC is not equilateral, then it is not equiangular.
Write the negation of the following.
Kanchanganga is in India and Everest is in Nepal.
Write the negation of the following statement.
7 is prime number and Tajmahal is in Agra.
Write the negation of the following statement.
I will have tea or coffee.
If p → q is an implication, then the implication ∼ q → ∼ p is called its
The negation of the statement (p ˄ q) `→` (r ˅ ∼ p) is ______.
Find the negation of 10 + 20 = 30
Write the following compound statements symbolically.
Triangle is equilateral or isosceles
Without using truth table prove that:
~ (p ∨ q) ∨ (~ p ∧ q) ≡ ~ p
Write the following statements in symbolic form
Milk is white if and only if the sky is not blue
Write the following statements in symbolic form
If Kutab – Minar is in Delhi then Taj - Mahal is in Agra
Write the following statements in symbolic form
Even though it is not cloudy, it is still raining
Using truth table prove that p ˅ (q ˄ r) ≡ (p ˅ q) ˄ (p ˅ r)
Write the negation of p → q
Choose the correct alternative:
Negation of p → (p ˅ ~q) is
Choose the correct alternative:
A biconditional statement is the conjunction of two ______ statements
Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”
Write the following statements in symbolic form.
If Qutub – Minar is in Delhi then Taj-Mahal is in Agra
Given 'p' and 'q' as true and 'r' as false, the truth values of p v (q ∧ ~r) and (p → r) ∧ q are respectively
If p, q are true statement and r is false statement, then which of the following statements is a true statement.
The symbolic form of the following circuit is (where p, q represents switches S1 and S2 closed respectively)
Which of the following is NOT true for p → q.
The Boolean expression ∼(q ⇒ ∼p) is equivalent to: ______
The negation of ∼s ∨ (∼r ∧ s) is equivalent to ______
The statement, 'If I go to school, then I will get knowledge' is equivalent to ______
Let p, q and r be any three logical statements. Which of the following is true?
Which of the following is logically equivalent to `∼(∼p \implies q)`?
Express the following compound statement symbolically:
Delhi is in India but Dhaka is not in Sri Lanka
Write the contrapositive of the inverse of the statement:
‘If two numbers are not equal, then their squares are not equal’.
Write the negation of (p `leftrightarrow` q).
Using truth table prove that:
~ (p `leftrightarrow` q) ≡ (p ∧ ~ q) ∨ (q ∧ ~ p)
Construct the truth table for the statement pattern:
[(p → q) ∧ q] → p
