Advertisements
Advertisements
प्रश्न
Construct the truth table of the following:
[(∼p ∨ q) ∧ (q → r)] → (p → r)
Advertisements
उत्तर
| p | q | r | ∼p | ∼p ∨ q | q→r | (∼p∨q) ∧ (q→r) | p→r | [(∼p∨q) ∧ (q→r)] → (p→r) |
| T | T | T | F | T | T | T | T | T |
| T | T | F | F | T | F | F | F | T |
| T | F | T | F | F | T | F | T | T |
| T | F | F | F | F | T | F | F | T |
| F | T | T | T | T | T | T | T | T |
| F | T | F | T | T | F | F | T | T |
| F | F | T | T | T | T | T | T | T |
| F | F | F | T | T | T | T | T | T |
APPEARS IN
संबंधित प्रश्न
Using truth table prove that p ↔ q = (p ∧ q) ∨ (~p ∧ ~q).
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
Construct the truth table of the following statement pattern.
(∼ p → ∼ q) ∧ (∼ q → ∼ p)
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]
Determine the truth values of p and q in the following case:
(p ∧ q) is F and (p ∧ q) → q is T
Write the truth value of the following statement.
A quadratic equation has two distinct roots or 6 has three prime factors.
Write the truth value of the negation of the following statement.
London is in England.
Write the following statement in symbolic form.
Even though it is not cloudy, it is still raining.
Write the following statement in symbolic form.
If Kutub-Minar is in Delhi then Taj-Mahal is in Agra.
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.
If Sunday is not holiday then Ram studies on holiday.
If p : He swims
q : Water is warm
Give the verbal statement for the following symbolic statement.
~ (p ∨ q)
If p : He swims
q : Water is warm
Give the verbal statement for the following symbolic statement.
q ∧ ~ p
State whether the following statement is True or False:
The negation of 10 + 20 = 30 is, it is false that 10 + 20 ≠ 30.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
3 is prime number if 3 is perfect square number.
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.
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.
Even though it is not cloudy, it is still raining.
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 ∨ r)
Rewrite the following statement without using conditional –
(Hint : p → q ≡ ∼ p ∨ q)
If price increases, then demand falls.
Write the negation of the following.
Ramesh is intelligent and he is hard working.
Rewrite the following statement without using the connective ‘If ... then’.
If a quadrilateral is rhombus then it is not a square.
Rewrite the following statement without using the connective ‘If ... then’.
If 10 − 3 = 7 then 10 × 3 ≠ 30.
Consider the following statements.
- If D is dog, then D is very good.
- If D is very good, then D is dog.
- If D is not very good, then D is not a dog.
- If D is not a dog, then D is not very good.
Identify the pairs of statements having the same meaning. Justify.
Write the negation of the following statement.
10 > 5 and 3 < 8
Negation of p → (p ˅ ∼ q) is ______
Find the negation of 10 + 20 = 30
Write the following compound statements symbolically.
Triangle is equilateral or isosceles
Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”
Write the following statement in symbolic form:
Milk is white if and only if the sky is not blue.
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)
State whether the following statement is True or False:
The converse of inverse of ~ p → q is q → ~ p
If c denotes the contradiction then the dual of the compound statement ∼p ∧ (q ∨ c) is ______
Let p : 7 is not greater than 4 and q : Paris is in France by two statements. Then ∼(p ∨ q) is the statement ______
Let S be a non-empty subset of R. Consider the following statement:
p: There is a rational number x ∈ S such that x > 0. Which of the following statements is the negation of the statement p?
The negation of the statement: "Getting above 95% marks is a necessary condition for Hema to get admission in good college'' is ______
Let p, q and r be any three logical statements. Which of the following is true?
If p : A man is happy, q : A man is rich, then the symbolic form of ‘A man is neither happy nor rich is ______.
Write the contrapositive of the inverse of the statement:
‘If two numbers are not equal, then their squares are not equal’.
From the following set of statements, select two statements which have similar meaning.
- If a man is judge, then he is honest.
- If a man is not a judge, then he is not honest.
- If a man is honest, then he is a judge.
- If a man is not honest, then he is not a judge.
If p, q are true statements and r, s are false statements, then write the truth value of the compound statement
(p `→` ∼ r) `→` (q ∧ s)
