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 that ∼p ˄ q ≡ (p ˅ q) ˄ ∼p
Using the truth table, prove the following logical equivalence :
p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)
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.
The angle is right angle if and only if it is of measure 90°.
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:
[(p ∧ q) ∨ r] ∧ [∼r ∨ (p ∧ q)]
Express the following statement in symbolic form.
Mango is a fruit but potato is a vegetable.
Express the following statement in symbolic form.
Milk is white or grass is green.
Write the negation of the following statement.
− 3 is a natural number.
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.
Find the truth value of the following statement.
Every accountant is free to apply his own accounting rules if and only if machinery is an asset.
Find the truth value of the following statement.
3 is a prime number and an odd number.
If p and q are true and r and s are false, find the truth value of the following compound statement.
(p → q) ∨ (r ∧ s)
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)
Fill in the blanks :
Conjunction of two statement p and q is symbolically written as ______.
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.
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 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 the question paper is not easy then we shall not pass.
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
Write the negation of the following.
Ramesh is intelligent and he is hard working.
Write the negation of the following.
Kanchanganga is in India and Everest is in Nepal.
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.
Rewrite the following statement without using the connective ‘If ... then’.
If it rains then the principal declares a holiday.
Write the negation of the following statement.
10 > 5 and 3 < 8
Write the negation of the following statement.
I will have tea or coffee.
Negation of p → (p ˅ ∼ q) is ______
Write the following compound statements symbolically.
Triangle is equilateral or isosceles
Write the following statement in symbolic form:
Milk is white if and only if the sky is not blue.
Without using truth table show that -
(p ˅ q) ˄ (∼p v ∼q) ≡ (p ∧ ∼q) ˄ (∼p ∧ q)
State whether the following statement is True or False:
The converse of inverse of ~ p → q is q → ~ p
Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”
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)
Let p : 7 is not greater than 4 and q : Paris is in France by two statements. Then ∼(p ∨ q) is the statement ______
The negation of (p ∨ ∼q) ∧ q is ______
The negation of the statement: "Getting above 95% marks is a necessary condition for Hema to get admission in good college'' is ______
Write the converse, inverse, and contrapositive of the statement. "If 2 + 5 = 10, then 4 + 10 = 20."
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)`?
Converse of the statement q `rightarrow` p is ______.
Write the following statement in symbolic form.
4 is an odd number if 3 is not a prime factor of 6.
Write the contrapositive of the inverse of the statement:
‘If two numbers are not equal, then their squares are not equal’.
